the representation dimension of a selfinjective algebra of euclidean type abstract we prove that the representation dimension of a selfinjective algebra of euclidean type is equal to three and give an explicit construction of the auslander generator of its module category

algebras of generalized quaternion type abstract we introduce and study the algebras of generalized quaternion type being natural generalizations of algebras which occurred in the study of blocks of group algebras with generalized quaternion defect groups we prove that all these algebras with 2 regular gabriel quivers are periodic algebras of period 4 and very specific deformations of the weighted surface algebras of triangulated surfaces with arbitrarily oriented triangles the main result of the paper forms an important step towards the morita equivalence classification of all periodic symmetric tame algebras of non polynomial growth applying the main result we establish existence of wild periodic algebras of period 4 with arbitrary large number at least 4 of pairwise non isomorphic simple modules these wild periodic algebras arise as stable endomorphism rings of cluster tilting cohen macaulay modules over one dimensional hypersurface singularities

periodicity of self injective algebras of polynomial growth abstract let a be an indecomposable representation infinite tame finite dimensional algebra of polynomial growth over an algebraically closed field we prove that a is a periodic algebra with respect to action of the bimodule syzygy operator if and only if a is morita equivalent to a socle deformation of an orbit algebra b g where b is the repetitive category of a tubular algebra b and g is an admissible infinite cyclic automorphism group of b the main contribution in the paper is to prove the sufficiency part of this equivalence it is known that every orbit algebra b g of a tubular algebra b admits a presentation as an orbit algebra t b r h of an r fold trivial extension algebra t b r of b with respect to free action of a finite cyclic automorphism group h of t b r a significant part of the paper is devoted to explicit descriptions of the minimal projective bimodule resolutions of properly chosen ten exceptional self injective algebras of polynomial growth and showing that all of them are periodic algebras then we deduce the periodicity of all algebras socle equivalent to the orbit algebras b g t b r h of tubular algebras b from the periodicity of these ten exceptional algebras using invariance of periodicity for finite galois coverings and derived equivalences of algebras

realizing stable categories as derived categories abstract in this paper we discuss a relationship between representation theory of graded self injective algebras and that of algebras of finite global dimension for a positively graded self injective algebra a such that a 0 has finite global dimension we construct two types of triangle equivalences first we show that there exists a triangle equivalence between the stable category of z graded a modules and the derived category of a certain algebra of finite global dimension secondly we show that if a has gorenstein parameter l then there exists a triangle equivalence between the stable category of z l z graded a modules and a derived orbit category of which is a triangulated hull of the orbit category of the derived category

resolutions of mesh algebras periodicity and calabi yau dimensions a triangulated category mathcal t sigma is said to be calabi yau of dimension d if d is a serre functor we determine which stable module categories of self injective algebras of finite type are calabi yau and compute their calabi yau dimensions correcting errors in previous work we first show that the calabi yau property of mod can be detected in the minimal projective resolution of the stable auslander algebra of over its enveloping algebra we then describe the beginning of such a minimal resolution for any mesh algebra of a stable translation quiver and apply covering theory to relate these minimal resolutions to those of the generalized preprojective algebras of dynkin graphs for representation finite self injective algebras of torsion order t 1 we obtain a complete description of their stable calabi yau properties but only partial results for those algebras of torsion order t 2 we also obtain some new information about the periods of the representation finite self injective algebras of torsion order t 1 finally we describe how these questions can also be approached by realizing the stable categories of representation finite self injective algebras as orbit categories of the bounded derived categories of hereditary algebras and illustrate this technique with several explicit computations that our previous methods left unsettled

a characterization of finite auslander reiten quivers a we give necessary and sufficient conditions for a finite k modulated translation quiver to be an auslander reiten quiver in terms of certain homology groups associated to the quiver section 3 b we show that whether a finite k modulated translation quiver is an auslander reiten quiver depends only on the underlying valued translation quiver and the characteristic of k and give necessary and sufficient conditions only in terms of the valued quiver and char k we also show that any valued quiver with valuations 1 n or n l n q 3 admits a modulation over any prime field sections 5 6 7 c to a valued translation quiver r we associate an unvalued translation quiver r i e all valuations are 1 and show that a finite k modulated translation quiver is an auslander reiten quiver if and only if the associated unvalued translation quiver with the trivial k modulation k prime field of k is an auslander reiten quiver section 8

some mean values related to the quasi arithmetic mean in this article we study new mean values and their properties related to the quasi arithmetic mean and their properties in the spirit of h haruki and th m rassias

fabrication adaptive optimization with an application to photonic crystal design it is often the case that the computed optimal solution of an optimization problem cannot be implemented directly irrespective of data accuracy because of either i technological limitations such as physical tolerances of machines or processes ii the deliberate simplification of a model to keep it tractable by ignoring certain types of constraints that pose computational difficulties and or iii human factors getting people to do the optimal solution motivated by this observation we present a modeling paradigm called fabrication adaptive optimization for treating issues of implementation fabrication we develop computationally focused theory and algorithms and we present computational results for incorporating considerations of implementation fabrication into constrained optimization problems that arise in photonic crystal design the fabrication adaptive optimization framework stems from the robust regularization of a function when the feasible region is not a normed space as typically encountered in application settings the fabrication adaptive optimization framework typically yields a nonconvex optimization problem in the special case where the feasible region is a finite dimensional normed space we show that fabrication adaptive optimization can be recast as an instance of modern robust optimization we study a variety of problems with special structures on functions feasible regions and norms for which computation is tractable and develop an algorithmic scheme for solving these problems in spite of the challenges of nonconvexity we apply our methodology to compute fabrication adaptive designs of two dimensional photonic crystals with a variety of prescribed features

configurations of trivial extensions of dynkin type a n for a given trivial extensionof cartan class dn we find a combinatorial algorithm giving the configuration of zdn associated to this algorithm is stated in the theorem 6 8 and illustrated in the example 6 3 in order to do that we develop an inductive embedding technique for the auslander reiten quiver of a trivial extensionof type dn this technique uses the ordinary quiver q which is the union of oriented cycles and a well known set of relationssuch thatis the quotient path algebra kq see 1 5 and 6 giving a trivial exten sion of type dn we get a trivial extensionof type dn m 1 by inserting a cycle with m vertices in one of the so called in sertion vertices of q in section 3 we describe the embedding of into this will allow us to deduce properties offrom and since q has less cycles that q we will use this embed ding to reduce the study ofto the minimal trivial extensions which were done in section 2

on krull gabriel dimension and galois coverings abstract assume that k is an algebraically closed field r a locally support finite locally bounded k category g a torsion free admissible group of k linear automorphisms of r and a r g we show that the krull gabriel dimension kg r of r equals the krull gabriel dimension kg a of a furthermore we determine the krull gabriel dimension of locally support finite repetitive k categories these results are applied to determine the krull gabriel dimension of standard selfinjective algebras of polynomial growth finally we show that there are no super decomposable pure injective modules over standard selfinjective algebras of domestic type

presentations of trivial extensions of finite dimensional algebras and a theorem of sheila brenner let be a finite dimensional algebra over an algebraically closed field such that any oriented cycle in the ordinary quiver of is zero in we describe the ordinary quiver and relations for t d the trivial extension of by its minimal injective cogenerator d and also for the repetitive algebra formula of associated with this description we give an application of a theorem of sheila brenner

stable calabi yau dimension of self injective algebras of finite type abstract we give an equivalent definition of the stable calabi yau dimension in terms of bimodule syzygies and so called stably inner automorphisms using it we complete the computation of the stable calabi yau dimensions of the self injective algebras of finite representation type which was started by k erdmann a skowronski j bialkowski and a dugas

auslander reiten components containing modules with bounded betti numbers let r be a connected selfinjective artin algebra and m an indecomposable nonprojective r module with bounded betti numbers lying in a regular component of the auslander reiten quiver of r we prove that the auslander reiten sequence ending at m has at most two indecomposable summands in the middle term furthermore we show that the component of the auslander reiten quiver containing m is either a stable tube or of type za we use these results to study modules with eventually constant betti numbers and modules with eventually periodic betti numbers

robust beamforming for cognitive multi antenna relay networks with bounded channel uncertainties in cognitive relay networks the interferences from secondary users sus and relays to primary users are constrained to be lower than a threshold the interference constraints are difficult to satisfy when the channel state information csi is imperfect in this paper we propose a robust beamforming scheme for the multi antenna non regenerative cognitive relay network where the multi antenna relay with imperfect csis helps the communication of single antenna su our objective is to design a robust beamforming scheme which maximizes the system capacity subject to transmit power constraint and interference constraints the bounded channel uncertainties are modeled using the worst case model the robust beamforming problem neglecting the correlation of channel uncertainties is reformulated as a convex semidefinite programming sdp by rank one relaxation this convex sdp is related with the worst case relay transmit power minimization problem which is further reformulated as a convex sdp whose rank one solution is proved to exist thus we propose the suboptimal solution to the robust beamforming problem which is found effectively by solving two convex sdps simulation results are provided to demonstrate the effectiveness of the proposed scheme

a characterization of selfinjective algebras of strictly canonical type abstract we prove that the class of selfinjective algebras of strictly canonical type investigated in kwiecien and skowronski 2009 27 kwiecien and skowronski 2009 28 coincides with the class of selfinjective algebras having triangular galois coverings with infinite cyclic group and the auslander reiten quiver with quasi tubes maximally saturated by simple and projective modules satisfying natural conditions

the symmetry period and calabi yau dimension of finite dimensional mesh algebras abstract within the class of finite dimensional mesh algebras we identify those which are symmetric and those whose stable module category is calabi yau we also give in combinatorial terms explicit formulas for the period of any such algebra where is the syzygy functor and for the calabi yau frobenius and the stable calabi yau dimensions when they are defined

self injective algebras and the second hochschild cohomology group abstract in this paper we study the second hochschild cohomology group hh 2 of a finite dimensional algebra in particular we determine hh 2 where is a finite dimensional self injective algebra of finite representation type over an algebraically closed field k and show that this group is zero for most such we give a basis for hh 2 in the few cases where it is not zero

on the support algebras of indecomposable modules over tame algebras of polynomial growth we investigate the support algebras of finite dimensional indecomposable modules over representation infinite tame algebras of polynomial growth over an algebraically closed field

embedding of the vertices of the auslander reiten quiver of an iterated tilted algebra of dynkin type δ in zδ abstract let be a dynkin diagram and k an algebraically closed field let a be an iterated tilted finite dimensional k algebra of type and denote by a its repetitive algebra we approach the problem of finding a combinatorial algorithm giving the embedding of the vertices of the auslander reiten quiver a of a in the auslander reiten quiver mod a z of the stable category mod a let t be a trivial extension of finite representation type and cartan class assume that we know the vertices of z corresponding to the radicals of the indecomposable projective t modules we determine the embedding of a in z for any algebra a such that t a t

telescope conjecture idempotent ideals and the transfinite radical the thesis studies the telescope conjecture for algebraic compactly generated triangulated categories the conjecture which says that every smashing localization of a compactly generated triangulated category is generated by compact objects is answered in affirmative in several cases main techniques to achieve this include homological algebra and basic set theoretic methods at the end a characterization for homotopy categories of complexes being compactly or more generally well generated is given for a wide class of additive categories

approximation algorithms for homogeneous polynomial optimization with quadratic constraints in this paper we consider approximation algorithms for optimizing a generic multi variate homogeneous polynomial function subject to homogeneous quadratic constraints such optimization models have wide applications e g in signal processing magnetic resonance imaging mri data training approximation theory and portfolio selection since polynomial functions are non convex the problems under consideration are all np hard in general in this paper we shall focus on polynomial time approximation algorithms in particular we first study optimization of a multi linear tensor function over the cartesian product of spheres we shall propose approximation algorithms for such problem and derive worst case performance ratios which are shown to be dependent only on the dimensions of the model the methods are then extended to optimize a generic multi variate homogeneous polynomial function with spherical constraint likewise approximation algorithms are proposed with provable approximation performance ratios furthermore the constraint set is relaxed to be an intersection of co centered ellipsoids namely we consider maximization of a homogeneous polynomial over the intersection of ellipsoids centered at the origin and propose polynomial time approximation algorithms with provable worst case performance ratios numerical results are reported illustrating the effectiveness of the approximation algorithms studied

robust convex optimization we study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set u yet the constraints must hold for all possible values of the data from u the ensuing optimization problem is called robust optimization in this paper we lay the foundation of robust convex optimization in the main part of the paper we show that if u is an ellipsoidal uncertainty set then for some of the most important generic convex optimization problems linear programming quadratically constrained programming semidefinite programming and others the corresponding robust convex program is either exactly or approximately a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods

on new classes of nonnegative symmetric tensors in this paper we introduce three new classes of nonnegative forms or equivalently symmetric tensors and their extensions the newly identified nonnegative symmetric tensors constitute distinctive convex cones in the space of general symmetric tensors order six or above for the special case of quartic forms they collapse into the set of convex quartic homogeneous polynomial functions we discuss the properties and applications of the new classes of nonnegative symmetric tensors in the context of polynomial and tensor optimization numerical experiments for solving certain polynomial optimization models based on the new classes of nonnegative symmetric tensors are presented

positive galois coverings of self injective algebras abstract in the article we study the structure of galois coverings of self injective artin algebras with infinite cyclic galois groups in particular we characterize all basic connected self injective artin algebras having galois coverings by the repetitive algebras of basic connected artin algebras and with the galois groups generated by positive automorphisms of the repetitive algebras

on distributional robust probability functions and their computations abstract consider a random vector and assume that a set of its moments information is known among all possible distributions obeying the given moments constraints the envelope of the probability distribution functions is introduced in this paper as distributional robust probability function we show that such a function is computable in the bi variate case under some conditions connections to the existing results in the literature and its applications in risk management are discussed as well

positivity of riesz functionals and solutions of quadratic and quartic moment problems abstract we employ positivity of riesz functionals to establish representing measures or approximate representing measures for truncated multivariate moment sequences for a truncated moment sequence y we show that y lies in the closure of truncated moment sequences admitting representing measures supported in a prescribed closed set k r n if and only if the associated riesz functional l y is k positive for a determining set k we prove that if l y is strictly k positive then y admits a representing measure supported in k as a consequence we are able to solve the truncated k moment problem of degree k in the cases i n k 2 4 and k r 2 ii n 1 k 2 and k is defined by one quadratic equality or inequality in particular these results solve the truncated moment problem in the remaining open cases of hilbert s theorem on sums of squares

relative singularity categories i auslander resolutions abstract let r be an isolated gorenstein singularity with a non commutative resolution a end r r m in this paper we show that the relative singularity category r a of a has a number of pleasant properties such as being hom finite moreover it determines the classical singularity category d s g r of buchweitz and orlov as a certain canonical quotient category if r has finite cm type which includes for example kleinian singularities then we show the much more surprising result that d s g r determines r aus r where aus r is the corresponding auslander algebra the proofs of these results use dg algebras a koszul duality and the new concept of dg auslander algebras which may be of independent interest

multivariate nonnegative quadratic mappings in this paper we study several issues related to the characterization of specific classes of multivariate quadratic mappings that are nonnegative over a given domain with nonnegativity defined by a prespecified conic order in particular we consider the set cone of nonnegative quadratic mappings defined with respect to the positive semidefinite matrix cone and study when it can be represented by linear matrix inequalities we also discuss the applications of the results in robust optimization especially the robust quadratic matrix inequalities and the robust linear programming models in the latter application the implementational errors of the solution are taken into account and the problem is formulated as a semidefinite program

robust solutions to uncertain semidefinite programs in this paper we consider semidefinite programs sdps whose data depend on some unknown but bounded perturbation parameters we seek robust solutions to such programs that is solutions which minimize the worst case objective while satisfying the constraints for every possible value of parameters within the given bounds assuming the data matrices are rational functions of the perturbation parameters we show how to formulate sufficient conditions for a robust solution to exist as sdps when the perturbation is full our conditions are necessary and sufficient in this case we provide sufficient conditions which guarantee that the robust solution is unique and continuous holder stable with respect to the unperturbed problem s data the approach can thus be used to regularize ill conditioned sdps we illustrate our results with examples taken from linear programming maximum norm minimization polynomial interpolation and integer programming

selfinjective algebras with hereditary stable slice abstract we determine the structure of all finite dimensional selfinjective algebras over a field whose auslander reiten quiver admits a hereditary stable slice

robust mimo cognitive radio via game theory cognitive radio cr systems improve the spectral efficiency by allowing the coexistence in harmony of primary users pus the legacy users with secondary users sus this coexistence is built on the premises that no su can generate interference higher than some prescribed limits against pus the system design based on perfect channel state information csi can easily end up violating the interference limits in a realistic situation where csi may be imperfect in this paper we propose a robust design of cr systems composed of multiple pus and multiple noncooperative sus in either single input single output siso frequency selective channels or more general multiple input multiple output mimo channels we formulate the design of the su network as a noncooperative game where the sus compete with each other over the resources made available by the pus by maximizing their own information rates subject to the transmit power and robust interference constraints following the philosophy of the worst case robustness we take explicitly into account the imperfectness of su to pu csi by adopting proper interference constraints that are robust with respect to the worst channel errors relying on the variational inequality theory we study the existence and uniqueness properties of the nash equilibria of the resulting robust games and devise totally asynchronous and distributed algorithms along with their convergency properties we also propose efficient numerical methods based on decomposition techniques to compute the robust transmit strategy for each su

lorentz positive maps and quadratic matrix inequalities with applications to robust miso transmit beamforming consider a unicast downlink beamforming optimization problem with robust signal to interference plus noise ratio constraints to account for imperfect channel state information at the base station in a multiple input single output miso communication system the convexity of this robust beamforming problem remains unknown a slightly conservative version of the robust beamforming problem is thus studied herein as a compromise it is in the form of a semi infinite second order cone program socp and more importantly it possesses an equivalent and explicit convex reformulation due to a linear matrix inequality lmi description of the cone of lorentz positive maps hence the conservative robust beamforming problem can be efficiently solved by an optimization solver additional robust shaping constraints can also be easily handled to control the amount of interference generated on other co existing users such as in cognitive radio systems

on auslander reiten components of blocks and self injective biserial algebras we investigate the existence of auslander reiten components of euclidean type for special biserial self injective algebras and for blocks of group algebras in particular we obtain a complete description of stable auslander reiten quivers for the tame self injective algebras considered here

the relationship between homological properties and representation theoretic realization of artin algebras we will study the relationship of quite different object in the theory of artin algebras namely auslander regular rings of global dimension two torsion theories categories and almost abelian categories we will apply our results to characterization problems of auslander reiten quivers 0 1 there exists a bijection between equivalence classes of krull schmidt categories c with additive generators m and morita equivalence classes of semiperfect rings which is given by c 7 c m m and the converse is given by 7 pr for the category pr of finitely generated projective modules although th is bijection itself is rather formal it will be very fruitful to study the relationship of a d below the object of this paper is to study it under the assumption that is an arti n algebra

some np complete problems in quadratic and nonlinear programming in continuous variable smooth nonconvex nonlinear programming we analyze the complexity of checking whether a a given feasible solution is not a local minimum and b the objective function is not bounded below on the set of feasible solutions we construct a special class of indefinite quadratic programs with simple constraints and integer data and show that checking a or b on this class is np complete as a corollary we show that checking whether a given integer square matrix is not copositive is np complete

on selfinjective algebras of finite representation type with maximal almost split sequences abstract we investigate the structure of finite dimensional selfinjective algebras of finite representation type over an arbitrary field having almost split sequences of modules whose middle term admits the maximal possible number of indecomposable direct summands

on compact exceptional objects in derived module categories abstract let a be a basic and connected finite dimensional algebra and d b a be the bounded derived category of finitely generated left a modules in this paper we consider lengths of tilting objects and indecomposable compact exceptional objects in d b a and prove a sufficient condition such that these lengths are bounded by the number of isomorphism classes of simple a modules moreover we show that algebras satisfying this criterion are bounded derived simple and describe an algorithm to construct a family of algebras satisfying this condition

a survey of the s lemma in this survey we review the many faces of the s lemma a result about the correctness of the s procedure the basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization convex geometry and linear algebra as well these were all active research areas but as there was little interaction between researchers in these different areas their results remained mainly isolated here we give a unified analysis of the theory by providing three different proofs for the s lemma and revealing hidden connections with various areas of mathematics we prove some new duality results and present applications from control theory error estimation and computational geometry

on a lattice like property of quasi arithmetic means abstract we will prove that every pair of quasi arithmetic means satisfying certain smoothness assumption has the supremum and the infimum in this set more precisely if f and g are c 2 functions with nowhere vanishing first derivative then there exists a function h such that i a f a h ii a g a h and iii for every continuous strictly monotone function s i r a f a s and a g a s implies a h a s a f stands for a quasi arithmetic mean moreover h c 2 h 0 and it is a solution of the differential equation h h max f f g g we also provide some extension to a finite family of means and dual reflected result

technical communique a stability and contractiveness analysis of discrete time markovian jump linear systems we propose performance criteria for discrete time linear systems with markov jumping parameters exact convex conditions for internal stability and contractiveness of such systems are expressed in terms of linear matrix inequalities these conditions are of the same form as that in the kalman yacubovich popov lemma

robust portfolio selection based on a multi stage scenario tree the aim of this paper is to apply the concept of robust optimization introduced by bel tal and nemirovski to the portfolio selection problems based on multi stage scenario trees the objective of our portfolio selection is to maximize an expected utility function value or equivalently to minimize an expected disutility function value as in a classical stochastic programming problem except that we allow for ambiguities to exist in the probability distributions along the scenario tree we show that such a problem can be formulated as a finite convex program in the conic form on which general convex optimization techniques can be applied in particular if there is no short selling and the disutility function takes the form of semi variance downside risk and all the parameter ambiguity sets are ellipsoidal then the problem becomes a second order cone program thus tractable we use sedumi to solve the resulting robust portfolio selection problem and the simulation results show that the robust consideration helps to reduce the variability of the optimal values caused by the parameter ambiguity

multiserial and special multiserial algebras and their representations abstract in this paper we study multiserial and special multiserial algebras these algebras are a natural generalization of biserial and special biserial algebras to algebras of wild representation type we define a module to be multiserial if its radical is the sum of uniserial modules whose pairwise intersection is either 0 or a simple module we show that all finitely generated modules over a special multiserial algebra are multiserial in particular this implies that in analogy to special biserial algebras being biserial special multiserial algebras are multiserial we then show that the class of symmetric special multiserial algebras coincides with the class of brauer configuration algebras where the latter are a generalization of brauer graph algebras we end by showing that any symmetric algebra with radical cube zero is special multiserial and so in particular it is a brauer configuration algebra

a generalization of gabriel s galois covering functors and derived equivalences abstract let g be a group acting on a category c we give a definition for a functor f c c to be a g covering and three constructions of the orbit category c g which generalizes the notion of a galois covering of locally finite dimensional categories with group g whose action on c is free and locally bonded defined by gabriel here c g is defined for any category c and we do not require that the action of g is free or locally bounded we show that a g covering is a universal g invariant functor and is essentially given by the canonical functor c c g by using this we improve a covering technique for derived equivalences also we prove theorems describing the relationships between smash product construction and the orbit category construction by cibils and marcos 2006 without the assumption that the g action is free the orbit category construction by a cyclic group generated by an auto equivalence modulo natural isomorphisms e g the construction of cluster categories is justified by a notion of the colimit orbit category in addition we give a presentation of the orbit category of a category with a monoid action by a quiver with relations which enables us to calculate many examples

exactness of sums of squares relaxations involving 3x3 matrices and lorentz cones we consider a family pm n of cones of positive maps and a semidefinite relaxation of these cones the cone pm n can be described as the set of those linear mappings from the space rm into the space of real symmetric n n matrices which map the m dimensional lorentz cone into the cone of real symmetric positive semidefinite matrices we describe the cone pm n as a cone of nonnegative polynomials in several variables we show that the considered semidefinite relaxation is in fact a sums of squares relaxation corresponding to this description of pm n our main result is that for n 3 the relaxation is exact hence it yields the exact result for optimisation problems over the cones pm 3 in particular the matrix ellipsoid problem for real symmetric 3 3 matrices can be rewritten as feasibility problem of a linear matrix inequality for m 4 n 4 there exist points in pm n which do not lie in the semidefinite set corresponding to the relaxation hence the relaxation is exact if and only if min n m 3

derived equivalences for tame weakly symmetric algebras having only periodic modules abstract recently a classification up to morita equivalence of all weakly symmetric algebras which have tame representation type simply connected galois coverings and all of whose modules are periodic equivalently the stable auslander reiten quiver consist only of tubes has been completed in j bialkowski a skowronski on tame weakly symmetric algebras having only periodic modules arch math to appear we classify in this paper these algebras up to derived equivalence and give a set of representatives for the derived equivalence classes

weighted surface algebras general version abstract we introduce the general weighted surface algebras of triangulated surfaces with arbitrarily oriented triangles and describe their basic properties in particular we prove that all these algebras except the singular disc triangle tetrahedral and spherical algebras are symmetric tame periodic algebras of period 4

algebras with cycle finite galois coverings we prove that the finite dimensional algebras over an algebraically closed field which admit cycle finite galois coverings with torsion free galois groups are of tame representation type and derive some consequences

higher dimensional auslander reiten theory on maximal orthogonal subcategories abstract we introduce the concept of maximal n 1 orthogonal subcategories over artin algebras and orders and develop n 1 dimensional auslander reiten theory on them we give the n auslander reiten translation and the n auslander reiten duality then show the existence of n almost split sequences and n fundamental sequences we give some examples

gluing derived equivalences together abstract the grothendieck construction of a diagram x of categories can be seen as a process to construct a single category gr x by gluing categories in the diagram together here we formulate diagrams of categories as colax functors from a small category i to the 2 category k cat of small k categories for a fixed commutative ring k in our previous paper we defined derived equivalences of those colax functors roughly speaking two colax functors x x i k cat are derived equivalent if there is a derived equivalence from x i to x i for all objects i in i satisfying some i equivariance conditions in this paper we glue the derived equivalences between x i and x i together to obtain a derived equivalence between grothendieck constructions gr x and gr x which shows that if colax functors are derived equivalent then so are their grothendieck constructions this generalizes and well formulates the fact that if two k categories with a g action for a group g are g equivariantly derived equivalent then their orbit categories are derived equivalent as an easy application we see by a unified proof that if two k algebras a and a are derived equivalent then so are the path categories a q and a q for any quiver q so are the incidence categories a s and a s for any poset s and so are the monoid algebras a g and a g for any monoid g also we will give examples of gluing of many smaller derived equivalences together to have a larger derived equivalence

d representation finite self injective algebras abstract in this paper we initiate the study of higher dimensional auslander reiten theory of self injective algebras we give a systematic construction of weakly d representation finite self injective algebras as orbit algebras of the repetitive categories of algebras of finite global dimension satisfying a certain finiteness condition for the serre functor the condition holds in particular for all fractionally calabi yau algebras of global dimension at most d this generalizes riedtmann s classical construction of representation finite self injective algebras our method is based on an adaptation of gabriel s covering theory for k linear categories to the setting of higher dimensional auslander reiten theory applications include n fold trivial extensions and classical and higher preprojective algebras which are shown to be d representation finite in many cases we also get a complete classification of all d representation finite self injective nakayama algebras for arbitrary d

τ2 stable tilting complexes over weighted projective lines abstract let x be a weighted projective line and coh x the associated category of coherent sheaves we classify the tilting complexes t in d b coh x such that 2 t t where is the auslander reiten translation in d b coh x as an application of this result we classify the 2 representation finite algebras which are derived equivalent to a canonical algebra this complements iyama oppermann s classification of the iterated tilted 2 representation finite algebras by passing to 3 preprojective algebras we obtain a classification of the selfinjective cluster tilted algebras of canonical type this complements ringel s classification of the selfinjective cluster tilted algebras

gorenstein versions of covering techniques for linear categories and their applications abstract let c be a g category for some group g we show that a g covering functor p c c g induces g precovering of their bounded derived categories singularity categories and gorenstein defect categories then we provide a gorenstein version of gabriel s theorem using this result we investigate the number of summands in a decomposition of the middle term of almost split sequences over monomial algebras

derived equivalences for φ auslander yoneda algebras in this paper we introduce auslander yoneda algebras in a triangulated category with a parameter set in n and present a method to construct new derived equivalences between these auslander yoneda algebras not necessarily artin algebras or their quotient algebras from a given almost stable derived equivalence as consequences of our method we have 1 suppose that a and b are representation finite self injective artin algebras with ax and by additive generators for a and b respectively if a and b are derived equivalent then the auslander yoneda algebras of x and y are derived equivalent for every admissible set in particular the auslander algebras of a and b are both derived equivalent and stably equivalent 2 for a self injective

a note on lack of strong duality for quadratic problems with orthogonal constraints abstract the general quadratically constrained quadratic program qqp is an important modelling tool for many diverse problems the qqp is in general np hard and numerically intractable lagrangian relaxations often provide good approximate solutions to these hard problems such relaxations are equivalent to semidefinite programming relaxations and can be solved efficiently for several special cases of qqp the lagrangian relaxation provides the exact optimal value this means that there is a zero duality gap and the problem is tractable it is important to know for which cases this is true since they can then be used as subproblems to improve lagrangian relaxation for intractable qqps in this paper we study the special qqp with orthogonal matrix constraints xx t i if c 0 the zero duality gap result holds if the redundant orthogonal constraints x t x i are added we show that this is not true in the general case however we show how to close the duality gap in the pure linear case by adding variables in addition to constraints

on the composition of homogeneous quasi arithmetic means abstract let 0 r strictly monotonic and continuous functions be the generators of the positively homogeneous quasi arithmetic means m m m and m the main result gives full characterizations of the functions and such that formula

noetherian hereditary abelian categories satisfying serre duality norwegian univ sci technol dept math sci n 7491 trondheim norway limburgs univ ctr dept wni b 3590 diepenbeek belgium reiten i norwegian univ sci technol dept math sci n 7491 trondheim norway

a mathsf d induced duality and its applications this paper attempts to extend the notion of duality for convex cones by basing it on a prescribed conic ordering and a fixed bilinear mapping this is an extension of the standard definition of dual cones in the sense that the nonnegativity of the inner product is replaced by a pre specified conic ordering defined by a convex cone mathsf d and the inner product itself is replaced by a general multi dimensional bilinear mapping this new type of duality is termed the mathsf d induced duality in the paper we further introduce the notion of mathsf d induced polar sets within the same framework which can be viewed as a generalization of the mathsf d induced dual cones and is convenient to use for some practical applications properties of the extended duality including the extended bi polar theorem are proven furthermore attention is paid to the computation and approximation of the mathsf d induced dual objects we discuss as examples applications of the newly introduced mathsf d induced duality concepts in robust conic optimization and the duality theory for multi objective conic optimization