deformed preprojective algebras of generalized dynkin type we introduce the class of deformed preprojective algebras of generalized dynkin graphs an n 1 d n n 4 eg e 7 eg and l n n 1 and prove that it coincides with the class of all basic connected finite dimensional self injective algebras for which the inverse nakayama shift v 1 s of every non projective simple module s is isomorphic to its third syzygy 3 s

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

a chebyshev method for the solution of boundary value problems abstract an expansion procedure using the chebyshev polynomials as base functions is proposed the method yields more accurate results than either of the galerkin or tau methods as indicated from solving the orr sommerfeld equation for both the plane poiseuille flow and the blasius velocity profile the chebyshev approximation is also applied to resolve the radial dependence of the flow field for a circular cylinder or a sphere in a uniform flow

modules without self extensions over gentle algebras abstract let x be a module over a gentle algebra such that ext 1 x x 0 then end x is up to morita equivalence a gentle algebra too

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

nonlinear stability of asymptotic suction the semigroup approach to the navier stokes equation in halfspace is used to prove that the stability of the asymptotic suction velocity profile is determined by the eigenvalues of the classical orr sommerfeld equation the usual obstacle namely that the corresponding linear operator contains 0 in the spectrum is removed with the use of weighted spaces 13 references

decorated marked surfaces part b topological realizations we study categories associated to a decorated marked surface mathbf s bigtriangleup which is obtained from an unpunctured marked surface mathbf s by adding a set of decorating points for any triangulation mathbf t of mathbf s bigtriangleup let gamma mathbf t be the associated ginzburg dg algebra we show that there is a bijection between reachable open arcs in mathbf s bigtriangleup and the reachable rigid indecomposables in the perfect derived category text per gamma mathbf t this is the dual of the bijection between simple closed arcs in mathbf s bigtriangleup and reachable spherical objects in the 3 calabi yau category mathcal d fd gamma mathbf t constructed in the prequel qiu in math ann 365 595 633 2016 moreover we show that amiot s quotient text per gamma mathbf t mathcal d fd gamma mathbf t that defines the generalized cluster categories corresponds to the forgetful map mathbf s bigtriangleup rightarrow mathbf s forgetting the decorating points in a suitable sense

endomorphism algebras for a class of negative calabi yau categories abstract we consider an orbit category of the bounded derived category of a path algebra of type a n which can be viewed as a m 1 cluster category for m 1 in particular we give a characterisation of those maximal m rigid objects whose endomorphism algebras are connected and then use it to explicitly study these algebras specifically we give a full description of them in terms of quivers and relations and relate them with higher cluster tilted algebras of type a as a by product we introduce a larger class of algebras called tiling algebras

f singularities under generic linkage abstract let r k x 1 x n be a polynomial ring over a prefect field of positive characteristic let i be an equi dimensional ideal in r and let j be a generic link of i in s r u i j c r we describe the parameter test submodule of s j in terms of the test ideal of the pair r i when a reduction of i is a complete intersection or almost complete intersection as an application we deduce a criterion for when s j has f rational singularities in these cases we also compare the f pure threshold of r i and s j

tagged mapping class groups auslander reiten translation we give a geometric realization the tagged rotation of the ar translation on the generalized cluster category associated to a surface mathbf s with marked points and non empty boundary which generalizes brustle zhang s result for the puncture free case as an application we show that the intersection of the shifts in the 3 calabi yau derived category mathrm mathcal d gamma mathbf s associated to the surface and the corresponding seidel thomas braid group of mathrm mathcal d gamma mathbf s is empty unless mathbf s is a polygon with at most one puncture i e of type a or d

a spectral galerkin approximation of the orr sommerfeld eigenvalue problem in a semi infinite domain the convergence of a galerkin approximation of the orr sommerfeld eigenvalue problem which is defined in a semi infinite domain is studied theoretically in case the system of trial functions is based on a composite of jacobi polynomials and an exponential transform of the semi infinite domain the error of the galerkin approximation is estimated in terms of the transformation parametera and the numbern of trial functions finite or infinite order convergence of the spectral galerkin method is obtained depending on how the transformation parameter is chosen if the transformation parameter is fixed then convergence is of finite order only however ifa is varied proportional to 1 n with an exponent 0 1 then the approximate eigenvalue converges faster than any finite power of 1 n asn some numerical examles are given

heights of ideals of minors we prove new height inequalities for determinantal ideals in a regular local ring or more generally in a local ring of given embedding codimension our theorems extend and sharpen results of faltings and bruns

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

derived equivalence classification of algebras of dihedral semidihedral and quaternion type abstract algebras of dihedral semidihedral and quaternion type were introduced by k erdmann as a generalization of blocks of finite groups of tame representation type in a series of papers erdmann gave a description of the morita equivalence classes of these algebras the aim of the present article is to present a classification of algebras of dihedral semidihedral and quaternion type up to derived equivalence as an application we can show that all basic algebras in erdmann s list are actually of tame representation type

on a cluster category of infinite dynkin type and the relation to triangulations of the infinity gon let k be a field and let d be a k linear algebraic triangulated category with split idempotents let be the suspension functor of d and let s be a 2 spherical object of d that is the morphism space d s i s is k for i 0 and i 2 and vanishes otherwise assume that s classically generates d that is each object of d can be built from s using de suspensions direct sums direct summands and distinguished triangles it was proved in 15 thm 2 1 that d is uniquely determined by these properties as we will explain d is a good candidate for a cluster category of dynkin type a for instance we show that there is a bijection between the cluster tilting subcategories of d and certain triangulations of the gon we use this to give an example of a subcategory a which is weak cluster tilting that is satisfies a 1a a but fails to be functorially finite perpendicular

rees algebras of modules we study rees algebras of modules within a fairly general framework we introduce an approach through the notion of bourbaki ideals that allows the use of deformation theory one can talk about the essentially unique generic bourbaki ideal i e of a module e which in many situations allows one to reduce the nature of the rees algebra of e to that of its bourbaki ideal i e properties such as cohen macaulayness normality and being of linear type are viewed from this perspective the known numerical invariants such as the analytic spread the reduction number and the analytic deviation of an ideal and its associated algebras are considered in the case of modules corresponding notions of complete intersection almost complete intersection and equimultiple modules are examined in some detail special consideration is given to certain modules which are fairly ubiquitous because interesting vector bundles appear in this way for these modules one is able to estimate the reduction number and other invariants in terms of the buchsbaum rim multiplicity

periodicity of d cluster tilted algebras abstract it is well known that any maximal cohen macaulay module over a hypersurface has a periodic free resolution of period 2 auslander reiten 1996 4 and buchweitz 1998 8 have used this periodicity to explain the existence of periodic projective resolutions over certain finite dimensional algebras which arise as stable endomorphism rings of cohen macaulay modules these algebras are in fact periodic meaning that they have periodic projective resolutions as bimodules and thus periodic hochschild cohomology as well the goal of this article is to generalize this construction of periodic algebras to the context of iyama s higher ar theory let c be a maximal d 1 orthogonal subcategory of an exact frobenius category b and start by studying the projective resolutions of finitely presented functors on the stable category c over both c and c under the assumption that c is fixed by d we show that d induces the 2 d th syzygy on mod c if c has finite type i e if c add t for a d cluster tilting object t then we show that the stable endomorphism ring of t has a quasi periodic resolution over its enveloping algebra moreover this resolution will be periodic if some power of d is isomorphic to the identity on c it follows in particular that 2 c y tilted algebras arising as stable endomorphism rings of cohen macaulay modules over curve singularities as in the work of burban iyama keller and reiten 2008 9 have periodic bimodule resolutions of period 4

purity of branch and critical locus abstract to a dominant morphism x s y s of n therian integral s schemes one has the inclusion c x y b x y of the critical locus in the branch locus of x y starting from the notion of locally complete intersection morphisms we give conditions on the modules of relative differentials x y x s and y s that imply bounds on the codimensions of c x y and b x y these bounds generalise to a wider class of morphisms the classical purity results for finite morphisms by zariski nagata auslander and faltings and grothendieck and van der waerden s purity for birational morphisms

coloured quivers for rigid objects and partial triangulations the unpunctured case we associate a coloured quiver to a rigid object in a hom finite 2 calabi yau triangulated category and to a partial triangulation on a marked unpunctured riemann surface we show that in the case where the category is the generalised cluster category associated to a surface the coloured quivers coincide we also show that compatible notions of mutation can be defined and give an explicit description in the case of a disk we show further that iyama yoshino reduction can be interpreted as cutting along an arc in the surface

algebras from surfaces without punctures abstract we introduce a new class of finite dimensional gentle algebras the surface algebras which are constructed from an unpunctured riemann surface with boundary and marked points by introducing cuts in internal triangles of an arbitrary triangulation of the surface we show that surface algebras are endomorphism algebras of partial cluster tilting objects in generalized cluster categories we compute the invariant of avella alaminos and geiss for surface algebras and we provide a geometric model for the module category of surface algebras

tame biserial algebras a similar result is suspected if we drop the property representationfinite in classes 1 and 2 and we will start an investigation of biserial algebras of infinite representation type the key to the result for representation finite algebras was to observe that each representation finite biserial algebra is special 13 see also the basic notations below which means that it can be presented by a quiver with nice relations special algebras play an important role in the modular representation theory of finite groups namely each representation finite block of a group algebra and some of the tame blocks they occur only in characteristic 2 are special 7 10 4 moreover in the complex representation theory of the lorentz group the so called harish chandra modules are defined over tame special algebras 6 in this paper we show that l a 62 for any special algebra a and that special algebras of infinite representation type are tame our paper consists of four parts first we prove that each special algebra is a factor of a special symmetric algebra theorem 1 5 for the latter the methods of gelfand and ponomarev used in the classification of the indecomposable harish chandra modules of the lorentz group apply and furnish a complete list of indecomposable finitely generated modules over special algebras proposition 2 3 presented in section 2 from this list we 480 0021 8693 85 3 00

special multiserial algebras are quotients of symmetric special multiserial algebras in this paper we give a new definition of symmetric special multiserial algebras in terms of defining cycles as a consequence we show that every special multiserial algebra is a quotient of a symmetric special multiserial algebra

stability of the laminar boundary layer in a streamwise corner this work examines the stability of viscous incompressible flow along a streamwise corner often called the corner boundary layer problem the semi infinite boundary value problem satisfied by small amplitude disturbances in the blending boundary layer region is obtained the mean secondary flow induced by the corner exhibits a flow reversal in this region uniformly valid first approximations to solutions of the governing differential equations are derived uniformity at infinity is achieved by a suitable choice of the large parameter and use of an appropriate langer variable approximations to solutions of balanced type have a phase shift across the critical layer which is associated with instabilities in the case of two dimensional boundary layer profiles viscous incompressible laminar flow along a streamwise corner formed by the intersection of two solid surfaces is often referred to as the corner boundary layer problem in the theoretical model of this problem two flat plates which are infinite in the streamwise and spanwise directions intersect such that the line of intersection the corner line is normal to the plane containing their leading edges the basic flow is along the line of intersection most theoretical work assumes a rectangular corner this situation is shown in figure 1

numerical solution of eigenvalue problems for linear boundary value odes abstract interrelationships between several popular approaches for solving eigenvalue problems for linear boundary value odes are given for linear eigenvalue problems the popular methods can be interpreted in a common framework this leads us to propose and justify alternative strategies the choice of numerical methods used here is motivated by the desire to solve eigenvalue problems for stiff odes in particular we consider a one step global method spline collocation and two initial value methods riccati and continuous orthonormalization to solve the orr sommerfeld equation a comparison of results for these methods using various implementation strategies is given

diophantine equations via cluster transformations abstract motivated by fomin zelevinsky s theory of cluster algebras we introduce a variant of the markov equation we show that all natural solutions of the equation arise from an initial solution by cluster transformations

exchange graphs and ext quivers abstract we study the oriented exchange graph eg n q of reachable hearts in the finite dimensional derived category d n q of the cy n ginzburg algebra n q associated to an acyclic quiver q we show that any such heart is induced from some heart in the bounded derived category d q via some lagrangian immersion l d q d n q we build on this to show that the quotient of eg n q by the seidel thomas braid group is the exchange graph ceg n 1 q of cluster tilting sets in the higher cluster category c n 1 q as an application we interpret buan thomas coloured quiver for a cluster tilting set in terms of the ext quiver of any corresponding heart in d n q

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

decorated marked surfaces spherical twists versus braid twists we are interested in the 3 calabi yau categories mathcal d arising from quivers with potential associated to a triangulated marked surface mathbf s without punctures we prove that the spherical twist group mathrm st of mathcal d is isomorphic to a subgroup generated by braid twists of the mapping class group of the decorated marked surface mathbf s bigtriangleup here mathbf s bigtriangleup is the surface obtained from mathbf s by decorating with a set of points where the number of points equals the number of triangles in any triangulations of mathbf s for instance when mathbf s is an annulus the result implies that the corresponding spaces of stability conditions on mathcal d are contractible

stability conditions and quantum dilogarithm identities for dynkin quivers abstract we study the fundamental groups of the exchange graphs for the bounded derived category d q of a dynkin quiver q and the finite dimensional derived category d n q of the calabi yau n ginzburg algebra associated to q in the case of d q we prove that its space of stability conditions in the sense of bridgeland is simply connected as an application we show that the donaldson thomas type invariant associated to q can be calculated as a quantum dilogarithm function on its exchange graph in the case of d n q we show that the faithfulness of the seidel thomas braid group action which is known for q of type a or n 2 implies the simply connectedness of the space of stability conditions

a reduction theorem for tau rigid modules we prove a theorem which gives a bijection between the support tilting modules over a given finite dimensional algebra a and the support tilting modules over a i where i is the ideal generated by the intersection of the center of a and the radical of a this bijection is both explicit and well behaved we give various corollaries of this with a particular focus on blocks of group rings of finite groups in particular we show that there are tilting finite wild blocks with more than one simple module we then go on to classify all support tilting modules for all algebras of dihedral semidihedral and quaternion type as defined by erdmann which include all tame blocks of group rings note that since these algebras are symmetric this is the same as classifying all basic two term tilting complexes and it turns out that a tame block has at most 32 different basic two term tilting complexes we do this by using the aforementioned reduction theorem which reduces the problem to ten different algebras only depending on the ground field k all of which happen to be string algebras to deal with these ten algebras we give a combinatorial classification of all rigid modules over not necessarily symmetric string algebras

order ideals and a generalized krull height theorem let n be a finitely generated module over a noetherian local ring r m we give criteria for the height of the order ideal n x of an element x n to be bounded by the rank of n the generalized principal ideal theorem of bruns eisenbud and evans says that this inequality always holds if x mn we show that the inequality even holds if the hypothesis becomes true after first extending scalars to some local domain and then factoring out torsion we give other conditions in terms of residual intersections and integral closures of modules we derive information about order ideals that leads to bounds on the heights of trace ideals of modules even in circumstances where we do not have the expected bounds for the heights of the order ideals

the orr sommerfeld equation on infinite intervals numerical and asymptotic methods have been developed the last several years to solve the orr sommerfeld os stability equation for boundary layers and other unbounded domain flows these are surveyed and some of the abstract mathematical questions they raise are mentioned there has been a conventional wisdom among fluid dynamicists that it has not been proved that the eigenvalues of the os equations are complete on an unbounded domain there is something to this since without the continuous spectrum which occurs for boundary layer flows the eigenvalues are not complete however much has been proved concerning the nature of the spectrum and the expansion properties of the generalized eigenfunctions the results of miklavcic and williams and of bakenko and herron form the core of the survey

eigenvalues of the orr sommerfeld equation in an unbounded domain on montre que dans l espace l 2 0 00 4 l equation generalisee d orr sommerfeld n a qu un nombre fini de valeurs propres lorsque l ecoulement moyen tend exponentiellement vers une constante

braid group actions on derived categories of coherent sheaves this paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety x the motivation for this is m kontsevich s homological mirror conjecture together with the occurrence of certain braid group actions in symplectic geometry one of the main results is that when dim x geq 2 our braid group actions are always faithful we describe conjectural mirror symmetries between smoothings and resolutions of singularities which lead us to find examples of braid group actions arising from crepant resolutions of various singularities relations with the mckay correspondence and with exceptional sheaves on fano manifolds are given moreover the case of an elliptic curve is worked out in some detail

generic modules for gentle algebras abstract in this article we construct the generic modules in each irreducible component of variety of dimensional modules of a triangular gentle algebra the construction is completely combinatorial and allows for determination of canonical decomposition of irreducible components as well as calculation of the dimension of the higher self extension spaces for generic modules

stable endomorphism algebras of modules over special biserial algebras we prove that the stable endomorphism algebra of a module without self extensions over a special biserial algebra is a gentle algebra in particular it is again special biserial as a consequence any algebra which is derived equivalent to a gentle algebra is gentle

codimension and connectedness of degeneracy loci over local rings we deduce results on the dimension and connectedness of degeneracy loci of maps of finite modules f m rightarrow n over a local noetherian ring a mathfrak m we show for instance that the expected determinantal bounds on the dimension of the t th degeneracy locus of f hold if f in mathfrak m mathrm hom m n and that this degeneracy locus is connected in the expected dimension provided hat a is a domain

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

cotorsion pairs in the cluster category of a marked surface abstract we study extension spaces cotorsion pairs and their mutations in the cluster category of a marked surface without punctures under the one to one correspondence between the curves valued closed curves in the marked surface and the indecomposable objects in the associated cluster category we prove that the dimension of extension space of two indecomposable objects in the cluster categories equals to the intersection number of the corresponding curves by using this result we prove that there are no non trivial t structures in the cluster categories when the surface is connected based on this result we give a classification of cotorsion pairs in these categories moreover we define the notion of paintings of a marked surface without punctures and their rotations they are a geometric model of cotorsion pairs and of their mutations respectively

the projective dimension of codimension two algebras presented by quadrics abstract motivated by a question of stillman we find a sharp upper bound for the projective dimension of ideals of height two generated by quadrics in a polynomial ring with arbitrary large number of variables we prove that ideals generated by n quadrics define cyclic modules with projective dimension at most 2 n 2 we refine this bound according to the multiplicity of the ideal we ask whether tight upper bounds for the projective dimension of ideals generated by quadrics can be expressed only in terms of their height and number of minimal generators

simplicial complexes and tilting theory for brauer tree algebras abstract we study 2 term tilting complexes of brauer tree algebras in terms of simplicial complexes we show the symmetry and convexity of the lattice polytope corresponding to the simplicial complex of 2 term tilting complexes via a geometric interpretation of derived equivalences we show that the f vector of the simplicial complexes of brauer tree algebras only depends on the number of the edges of the brauer trees and hence it is a derived invariant in particular this result implies that the number of 2 term tilting complexes which is in bijection with support tilting modules is a derived invariant moreover we apply our result to the enumeration problem of coxeter bicatalan combinatorics

auslander reiten components of symmetric special biserial algebras abstract we provide a combinatorial algorithm for constructing the stable auslander reiten component containing a given indecomposable module of a symmetric special biserial algebra using only information from its underlying brauer graph we also show that the structure of the auslander reiten quiver is closely related to the distinct green walks of the brauer graph and detail the relationship between the precise shape of the stable auslander reiten components for domestic brauer graph algebras and their underlying graph furthermore we show that the specific component containing a given simple or indecomposable projective module for any brauer graph algebra is determined by the edge in the brauer graph associated to the module

cohen macaulay differential graded modules and negative calabi yau configurations abstract in this paper we introduce the class of cohen macaulay cm dg differential graded modules over gorenstein dg algebras and study their basic properties we show that the category of cm dg modules forms a frobenius extriangulated category in the sense of nakaoka and palu and it admits almost split extensions we also study representation finite d self injective dg algebras a in detail for some positive integer d in particular we classify the auslander reiten ar quivers of cm a for a large class of d self injective dg algebras a in terms of d calabi yau cy configurations which are riedtmann s configurations for the case d 1 for any given d cy configuration c we show there exists a d self injective dg algebra a such that the ar quiver of cma is given by c for type a n by using a bijection between d cy configurations and certain purely combinatorial objects which we call maximal d brauer relations given by coelho simoes we construct such a through a brauer tree dg algebra

stability of mean flows over an infinite flat plate the present investigation is mainly concerned with a stability analysis for the linearized navier stokes equations for parallel and nonparallel mean flows over an infinite flat plate the system of equations for parallel flows is presented the system is viewed as a generalized orr sommerfeld equation attention is given to an explicit criterion characterizing the case when the stability of all physically reasonable solutions is determined by the eigenvalues the proof given in the investigation is applicable to both the generalized orr somerfeld equations and the modified equations for nonparallel flow the fact that the criterion is independent of the completeness or incompleteness of eigenfunctions is contrary to some expectations

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

classification of two term tilting complexes over brauer graph algebras using only the combinatorics of its defining ribbon graph we classify the two term tilting complexes as well as their indecomposable summands of a brauer graph algebra as an application we determine precisely the class of brauer graph algebras which are tilting discrete

trivial extensions of gentle algebras and brauer graph algebras abstract we show that two well studied classes of tame algebras coincide namely the class of symmetric special biserial algebras coincides with the class of brauer graph algebras we then explore the connection between gentle algebras and symmetric special biserial algebras by explicitly determining the trivial extension of a gentle algebra by its minimal injective co generator this is a symmetric special biserial algebra and hence a brauer graph algebra of which we explicitly give the brauer graph we further show that a brauer graph algebra gives rise via admissible cuts to many gentle algebras and that the trivial extension of a gentle algebra obtained via an admissible cut is the original brauer graph algebra as a consequence we prove that the trivial extension of a jacobian algebra of an ideal triangulation of a riemann surface with marked points in the boundary is isomorphic to the brauer graph algebra with brauer graph given by the arcs of the triangulation

on the invariant theory for acyclic gentle algebras in this paper we show that the fields of rational invariants over the irreducible components of the module varieties for an acyclic gentle algebra are purely transcendental extensions along the way we exhibit for such fields of rational invariants a transcendence basis in terms of schofield s determinantal semi invariants we also show that the moduli spaces of modules over regular irreducible component are just a products of projective spaces contents

on the lie algebra structure of the first hochschild cohomology of gentle algebras and brauer graph algebras abstract in this paper we determine the first hochschild homology and cohomology with different coefficients for gentle algebras and we give a geometrical interpretation of these co homologies using the ribbon graph of a gentle algebra as defined in 32 we give an explicit description of the lie algebra structure of the first hochschild cohomology of gentle and brauer graph algebras with multiplicity one based on trivial extensions of gentle algebras and we show how the hochschild cohomology is encoded in the brauer graph in particular we show that except in one low dimensional case the resulting lie algebras are all solvable

n angulated categories we dene n angulated categories by modifying the axioms of triangulated categories in a natural way we show that heller s parametrization of pre triangulations extends to pre n angulations we obtain a large class of examples of n angulated cate gories by considering n 2 cluster tilting subcategories of triangulated categories which are stable under the n 2 nd power of the suspension functor as an application we show how n angulated calabi yau categories yield triangulated calabi yau categories of higher calabi yau dimension finally we sketch a link to algebraic geometry and string theory

mapping cones in the bounded derived category of a gentle algebra abstract in this article we describe the triangulated structure of the bounded derived category of a gentle algebra by describing the triangles induced by the morphisms between indecomposable objects in a basis of their hom space

cluster tilting subcategories and torsion pairs in igusa todorov cluster categories of dynkin type a_ infty we give a combinatorial classification of cluster tilting subcategories and torsion pairs in igusa todorov cluster categories of dynkin type a infty

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

numerical exterior algebra and the compound matrix method the compound matrix method which was first proposed for numerically integrating systems of differential equations in hydrodynamic stability on k 2 3 dimensional subspaces of mathbb c n by using compound matrices as coordinates is reformulated in a coordinate free way using exterior algebra spaces bigwedge k mathbb c n