generic representation theory of quivers with relations abstract the irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra are explored with regard to both their geometry and the structure of the modules they encode provided that the base field is algebraically closed and has infinite transcendence degree over its prime field we establish the existence and uniqueness not up to isomorphism but in a strong sense to be specified of a generic module for any irreducible component c that is of a module which displays all categorically defined generic properties of the modules parametrized by c the crucial point of the existence statement a priori almost obvious lies in the description of such a module in a format accessible to representation theoretic techniques our approach to generic modules over path algebras modulo relations by way of minimal projective resolutions is largely constructive it is explicit for large classes of algebras of wild type we follow with an investigation of the properties of such generic modules in terms of quiver and relations the sharpest specific results on all fronts are obtained for truncated path algebras that is for path algebras of quivers modulo ideals generated by all paths of a fixed length this class of algebras extends the comparatively thoroughly studied hereditary case displaying many novel features

existence of weakly efficient solutions in nonsmooth vector optimization in this paper we study the existence of weakly efficient solutions for some nonsmooth and nonconvex vector optimization problems we consider problems whose objective functions are defined between infinite and finite dimensional banach spaces our results are stated under hypotheses of generalized convexity and make use of variational like inequalities

flat endofinite modules prime ideals and duality abstract bijective correspondences are established between endofinite injective left modules endofinite flat right modules finite collections of minimal noetherian prime ideals normalized rank functions on left ideals and characters endofinite flat modules are identified as flat covers of modules associated to a minimal noetherian prime ideal while endofinite flat injectives are characterized by localizations with a semiprimary qf 3 quotient ring

some model theory over hereditary noetherian domains questions in the model theory of modules over hereditary noetherian domains are investigated with particular attention being paid to differential polynomial rings and to generalized weyl algebras we prove that there exists no isolated point in the ziegler spectrum over a simple hereditary generalized weyl algebra a of the sort considered by bavula algebra i analiz 4 1 1992 75 97 over a field k with char k 0 the first weyl algebra a 1 k is one such and the category of finite length modules over a does not have any almost split sequence we show that the theory of all modules over a wide class of generalized weyl algebras and related rings interprets the word problem for groups and in the case that the field is countable there exists a superdecomposable pure injective module over a this class includes for example the universal enveloping algebra usl 2 k

endoproperties of modules and local duality abstract let r be any ring and n i i n i be a direct sum of finitely presented left r modules n i suppose that d n and d n i are the local duals of n and n i for each i i we prove that the lattice of endosubmodules of n is anti isomorphic to the lattices of matrix subgroups of d n and of m i i d n i as consequences n is endoartinian if and only if m or d n is endonoetherian and n is endonoetherian if and only if m or d n is pure injective we obtain in particular that if r is a krull schmidt ring and m is an indecomposable pure injective endonoetherian right r module which is the source of a left almost split morphism in mod r then m is endofinite as an application a ring r is of finite representation type if and only if every pure injective right r module is endonoetherian

the hom yang baxter equation hom lie algebras and quasi triangular bialgebras we study a twisted version of the yang baxter equation called the hom yang baxter equation hybe which is motivated by hom lie algebras three classes of solutions of the hybe are constructed one from hom lie algebras and the others from drinfeld s dual quasi triangular bialgebras each solution of the hybe can be extended to operators that satisfy the braid relations assuming an invertibility condition these operators give a representation of the braid group

hom lie 2 algebras abstract in this paper we introduce the notions of hom lie 2 algebras which is the categorification of hom lie algebras hl algebras which is the hom analogue of l algebras and crossed modules of hom lie algebras we prove that the category of hom lie 2 algebras and the category of 2 term hl algebras are equivalent we give a detailed study on skeletal hom lie 2 algebras in particular we construct the hom analogues of the string lie 2 algebras associated to any semisimple involutive hom lie algebras we also proved that there is a one to one correspondence between strict hom lie 2 algebras and crossed modules of hom lie algebras we give the construction of strict hom lie 2 algebras from hom left symmetric algebras and symplectic hom lie algebras

the endofinite spectrum of a tame algebra let r be a ring based on indecomposable endofinite r modules and characters that were introduced by crawley boevey modules of finite length over their endomorphism ring in s brenner h tachikawa eds representations of algebras and related topics in london math soc lecture note ser vol 168 1992 pp 127 184 we define the endofinite spectrum of the ring r we compute this spectrum in some examples and study the behaviour of it under certain functors with the objective of understanding the endofinite spectrum of tame algebras furthermore we show that the endomorphism ring of a minimal point of the endofinite spectrum is a skew field hence the minimal points belong to the cohn spectrum as studied by ringel the spectrum of a finite dimensional algebra in proc conf on ring theory dekker new york 1979 pp 535 598 which in turn is a subset of the endofinite spectrum finally we introduce the normalised endofinite spectrum

separable equivalence complexity and representation type abstract we generalise the notion of separable equivalence originally presented by linckelmann in 13 to an equivalence relation on additive categories we use this generalisation to show that from an initial equivalence between two algebras we may build equivalences between many related categories we also show that separable equivalence preserves the representation type of an algebra this generalises linckelmann s result in 13 where he showed this in the case of symmetric algebras we use these theorems to show that the group algebras of several small cyclic groups cannot be separably equivalent this gives several examples of algebras that have the same complexity but are not separably equivalent

deformations of lie algebras using σ derivations in this article we develop an approach to deformations of the witt and virasoro algebras based on sigma derivations we show that sigma twisted jacobi type identity holds for generators of such deformations for the sigma twisted generalization of lie algebras modeled by this construction we develop a theory of central extensions we show that our approach can be used to construct new deformations of lie algebras and their central extensions which in particular include naturally the q deformations of the witt and virasoro algebras associated to q difference operators providing also corresponding q deformed jacobi identities c 2005 elsevier inc all rights reserved

wild torsion modules over weyl algebras and general torsion modules over hnps let a 1 be the first weyl algebra over a field f of characteristic zero we show that the category of a 1 modules of finite length is wild despite the fact that every a 1 module of finite length is cyclic in fact the category of a 1 modules not necessarily finitely generated of socle height 2 is wild in a very strong sense among the applications we show i essentially any f algebra can occur as the endomorphism algebra of an a 1 module of socle height 2 ii a 1 has very large indecomposable modules of finite length iii there is an hnp hereditary noetherian prime ring that has indecomposable modules of finite length requiring arbitrary many generators we also complete the basic theory of finitely generated modules over general hnps by showing that every such module is a direct sum of right ideals and homomorphic images of right ideals and by proving a simultaneous decomposition theorem for an arbitrary projective module and submodule

nonsmooth multiple objective optimization in separable hilbert spaces abstract this paper provides new necessary and sufficient optimality conditions for nonsmooth multiple objective optimization programs in separable hilbert spaces

non isomorphic derived equivalent tubular curves and their associated tubular algebras abstract let r be the field of real numbers we construct two tubular canonical r algebras in the sense of c m ringel w crawley boevey 1990 in topics in algebra banach center publ no 26 pp 407 432 which are neither isomorphic nor dual to each other but which are tilting equivalent this relates to the fact that each of these algebras admits two distinct isomorphism classes of separating tubular families of standard stable tubes the results are derived from the existence of two non isomorphic tubular exceptional curves in the sense of h lenzing 1998 in trends in ring theory v dlab et al eds cms conf proc vol 22 pp 71 97 am math soc providence over r which are derived equivalent one having a commutative and the other a non commutative function field furthermore we classify all generic modules over such tubular algebras

representations up to homotopy of lie algebroids we introduce and study the notion of representation up to homotopy of a lie algebroid paying special attention to examples we use representations up to homotopy to define the adjoint representation of a lie algebroid and show that the resulting cohomology controls the deformations of the structure the weil algebra of a lie algebroid is defined and shown to coincide with kalkman s brst model for equivariant cohomology in the case of group actions the relation of this algebra with the integration of poisson and dirac structures is explained in arias abad crainic ann inst fourier

polyhedral groups mckay quivers and the finite algebraic groups with tame principal blocks given an algebraically closed field k of characteristic p 3 we classify the finite algebraic k groups whose algebras of measures afford a principal block of tame representation type the structure of such a group mathcal g is largely determined by a linearly reductive subgroup scheme hat mathcal g of sl 2 with the mckay quiver of hat mathcal g relative to its standard module being the gabriel quiver of the principal block mathcal b 0 mathcal g the graphs underlying these quivers are extended dynkin diagrams of type tilde a tilde d or tilde e and the tame blocks are morita equivalent to generalizations of the trivial extensions of the radical square zero tame hereditary algebras of the corresponding type

vector continuous time programming without differentiability in this work continuous time programming problems of vector optimization are considered firstly a nonconvex generalized gordan s transposition theorem is obtained then the relationship with the associated weighting scalar problem is studied and saddle point optimality results are established a scalar dual problem is introduced and duality theorems are given no differentiability assumption is imposed

canonical matrices for linear matrix problems abstract we consider a large class of matrix problems which includes the problem of classifying arbitrary systems of linear mappings for every matrix problem from this class we construct belitskii s algorithm for reducing a matrix to a canonical form which is the generalization of the jordan normal form and study the set c mn of indecomposable canonical m n matrices considering c mn as a subset in the affine space of m n matrices we prove that either c mn consists of a finite number of points and straight lines for every m n or c mn contains a 2 dimensional plane for a certain m n

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

generalized convexity in multiobjective programming abstract for the scalar programming problem some characterizations for optimal solutions are known in these characterizations convexity properties play a very important role in this work we study characterizations for multiobjective programming problem solutions when functions belonging to the problem are differentiable these characterizations need some conditions of convexity in differentiable scalar programming problems the concept of invexity is very important we prove that it is also necessary for the multiobjective programming problem and give some characterizations of multiobjective programming problem solutions under weaker conditions we define analogous concepts to those of stationary points and to the conditions of kuhn tucker and fritz john for the multiobjective programming problem

parameter curves for the regular representations of tame bimodules abstract we present results and examples which show that the consideration of a certain tubular mutation is advantageous in the study of noncommutative curves which parametrize the simple regular representations of a tame bimodule we classify all tame bimodules where such a curve is actually commutative or in different words where the unique generic module has a commutative endomorphism ring this extends results from d kussin noncommutative curves of genus zero related to finite dimensional algebras mem amer math soc in press to arbitrary characteristic in characteristic two additionally inseparable cases occur further results are concerned with autoequivalences fixing all objects but not isomorphic to the identity functor

hom associative algebras up to homotopy abstract a hom associative algebra is an algebra whose associativity is twisted by an algebra homomorphism in this paper we introduce a strongly homotopy version of hom associative algebras h a algebras in short on a graded vector space we describe 2 term h a algebras in detail in particular we study skeletal and strict 2 term h a algebras we also introduce hom associative 2 algebras as categorification of hom associative algebras the category of 2 term h a algebras and the category of hom associative 2 algebras are shown to be equivalent next we define a suitable hochschild cohomology theory for h a algebras which control the deformation of the structures finally we visit h l algebras introduced by sheng and chen and show that an appropriate skew symmetrization of h a algebras give rise to h l algebras

relative formality theorem and quantisation of coisotropic submanifolds we prove a relative version of kontsevich s formality theorem this theorem involves a manifold m and a submanifold c and reduces to kontsevich s theorem if c m it states that the dgla of multivector fields on an infinitesimal neighbourhood of c is l quasiisomorphic to the dgla of multidifferential operators acting on sections of the exterior algebra of the conormal bundle applications to the deformation quantisation of coisotropic submanifolds are given the proof uses a duality transformation to reduce the theorem to a version of kontsevich s theorem for supermanifolds which we also discuss in physical language the result states that there is a duality between the poisson sigma model on a manifold with a d brane and the poisson sigma model on a supermanifold without branes or more properly with a brane which extends over the whole supermanifold

preinvex functions and weak efficient solutions for some vectorial optimization problem in banach spaces in this work we introduce the notion of preinvex function for functions between banach spaces by using these functions we obtain necessary and sufficient conditions of optimality for vectorial problems with restrictions of inequalities moreover we will show that this class of problems has the property that each local optimal solution is in fact global

multi objective infinite programming using the theory of abstract optimization problems in infinite dimensional spaces we provide necessary optimality conditions of first and second order for weakly efficient solutions of the multi objective infinite programming problem sufficient conditions are given under invexity assumptions we generalize the notion of kkt invexity for the multi objective infinite problem and show that this notion is a necessary and sufficient condition for every vector kkt solution to be a weakly efficient solution moreover we develop a theorem of the alternative useful for proving some of our results

generic modules of tame algebras over real closed fields abstract given a generically tame finite dimensional algebra over a real closed field we describe the relations between the infinite families of indecomposable modules with bounded dimension and the generic modules these are similar to those occurring for the algebraically closed field case but the parametrizations are obtained over five particular centrally bounded principal ideal domains instead of over rational algebras

on the sparsity of representations of rings of pure global dimension zero it is shown that the rings r all of whose left modules are direct sums of finitely generated modules satisfy the following finiteness condition for each positive integer n there are only finitely many isomorphism types of a indecomposable left r modules of length n b finitely presented indecomposable right r modules of length n c indecomposable right r modules having minimal projective resolutions with n relations moreover our techniques yield a very elementary proof for the fact that the presence of the above decomposability hypothesis for both left and right r modules entails finite representation type

some vector optimization problems in banach spaces with generalized convexity abstract in this paper we consider a vector optimization problem where all functions involved are defined on banach spaces new classes of generalized type i functions are introduced for functions between banach spaces based upon these generalized type i functions we obtain a few sufficient optimality conditions and prove some results on duality

representations of a k algebra over the rational functions over k abstract for a finite dimensional k algebra k a field we study the relations between the category of all left modules mod and the category of finitely generated kk x k x modules mod k x in particular we consider those g mod k x such that g is indecomposable we prove that such modules are in the mouth of components in mod k x which are tubes or have the shape z a z d or z b

jacobian algebras with periodic module category and exponential growth abstract recently it was proven by geiss labardini fragoso and schroer in 1 that every jacobian algebra associated to a triangulation of a closed surface s with a collection of marked points m is tame and ladkani proved in 2 these algebras are weakly symmetric in this work we show that for these algebras the auslander reiten translation acts 2 periodically on objects moreover we show that excluding only the case of a sphere with 4 or less punctures these algebras are of exponential growth these results imply that the existing characterization of symmetric tame algebras whose non projective indecomposable modules are periodic has at least a missing class see 3 theorem 6 2 or 4 as a consequence of the 2 periodical actions of the auslander reiten translation on objects we have that the auslander reiten quiver of the generalized cluster category c s m consists only of stable tubes of rank 1 or 2

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

the gap function for optimization problems in banach spaces abstract in this paper some properties of the gap function for multiple objective optimization problems in banach spaces are established

on generically tame algebras over perfect fields abstract given a generically tame finite dimensional algebra over an infinite perfect field we give for each natural number d parametrizations of the indecomposable modules with dimension d similar to those occurring for the algebraically closed field case we parametrize over bounded principal ideal domains instead of over rational algebras

proper efficiency conditions and duality results for nonsmooth vector optimization in banach spaces under φ ρ invexity abstract in this paper a new class of nonsmooth nonconvex multiobjective programming problems in banach spaces is considered the sufficient optimality conditions for efficiency and proper efficiency are established under nonsmooth invexity and generalized invexity notions after extending these concepts to the functions between banach spaces further mond weir duality theorems are also established under invexity for the considered vector optimization problems in banach spaces

invexity and the kuhn tucker theorem abstract it is pointed out that type 1 invex functions are the most general class of functions relevant to necessary and sufficient conditions for kuhn tucker optimality in nonlinear programming linear programming duality is used to show an equivalence between the concept of invexity and the kuhn tucker conditions for optimality the invexity kernel and the lagrange multiplier y in the kuhn tucker theory are dual variables the kuhn tucker conditions are necessary conditions for optimality provided that certain constraint qualifications apply a particular result given here is that invexity in itself constitutes an appropriate constraint qualification

deformation theory of infinity algebras abstract this work explores the deformation theory of algebraic structures in a very general setting these structures include associative algebras lie algebras and the infinity versions of these structures the strongly homotopy associative and lie algebras in all these cases the algebraic structure is determined by an element of a certain graded lie algebra which determines a differential on the lie algebra we work out the deformation theory in terms of the lie algebra of coderivations of an appropriate coalgebra structure and construct a universal infinitesimal deformation as well as a miniversal formal deformation by working at this level of generality the main ideas involved in deformation theory stand out more clearly