pure injectives and the spectrum of the cohomology ring of a finite group for a finite group g and a field k of prime characteristic we study certain pure injective kg modules in terms of the spectrum of the group cohomology ring hog ku for instance we construct a map from the projective variety projhog ku to the ziegler spectrum of indecomposable pure injective kg modules we identify the module corre sponding to a generic point for a component of the variety it is generic in the sense of crawley boevey and closely related to a certain rickard idempotent module we include also a complete classification of all kg modules which arise as a direct summand of a possibly infinite product of syzygies of the trivial module k

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

representation dimension and finitely generated cohomology abstract we consider selfinjective artin algebras whose cohomology groups are finitely generated over a central ring of cohomology operators for such an algebra we show that the representation dimension is strictly greater than the maximal complexity occurring among its modules this provides a unified approach to computing lower bounds for the representation dimension of group algebras exterior algebras and artin complete intersections we also obtain new examples of classes of algebras with arbitrarily large representation dimension

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

representation type of hecke algebras of type a in this paper we provide a complete classification of the representation type for the blocks for the hecke algebra of type a stated in terms of combinatorical data the computation of the complexity of young modules is a key component in the proof of this classification result

velocity analysis based on minimum entropy seismic resolution is determined by the sparsity of reflection events together with the dispersion of the wavelets representing those events in this paper minimum entropy me norms are introduced as a measure of spatial resolving power it is shown that the lateral dispersion of inverted diffractor responses inverted spatial wavelets increases with increasing velocity error using this property minimum entropy velocity analysis meva is proposed to extract velocity information from diffraction energy meva can be successfully applied to zero offset including poststack data and common offset data with a sufficient amount of diffraction energy in addition meva can be used as an alternative to existing cmp velocity estimation techniques

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

stability and asymptotic stability in the energy space of the sum of n solitons for subcritical gkdv equations we prove in this paper the stability and asymptotic stability in h1 of a decoupled sum of n solitons for the subcritical generalized kdv equations the proof of the stability result is based on energy arguments and monotonicity of the local l2 norm note that the result is new even for p 2 the kdv equation the asymptotic stability result then follows directly from a rigidity theorem in 16

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 lyapunov stability of the n soliton solutions in the lax hierarchy of the benjamin ono equation the lyapunov stability is established for the n soliton solutions in the lax hierarchy of the benjamin ono bo equation we characterize the n soliton profiles as critical points of certain lyapunov functional by using several results derived by the inverse scattering transform of the bo equation we demonstrate the convexity of the lyapunov functional when evaluated at the n soliton profiles from this fact we deduce that the n soliton solutions are energetically stable

migration velocity analysis by wave field extrapolation velocity information is essential to both common midpoint cmp stacking and migration cmp stacking provides the basis for conventional velocity estimation techniques in that for a number of trial velocities the stack response of a cmp gather is computed and displayed in the form of a velocity table an alternative approach to velocity estimation makes use of the basic ingredients of migration downward extrapolation and imaging of seismic wave fields the procedure involves migration of a cmp gather with a number of trial velocities and collection of the zero offset information again in the form of a velocity table operating on a cmp gather the migration based approach produces results similar to those of the conventional method analyses of synthetic cmp gathers using both methods show essentially equivalent treatments of seismic signal and similar dependence of accuracy and resolving power on recording geometry we have extended the migration based approach to include more than one cmp gather in

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

radical embeddings and representation dimension given a representation finite algebra b and a subalgebra a of b such that the jacobson radicals of a and b coincide we prove that the representation dimension of a is at most three by a result of igusa and todorov this implies that the finitistic dimension of a is finite

canonical forms of pairs of complex matrices abstract using methods of the representation theory of finite dimensional associative algebras the paper presents an explicit classification of the pairs of real subspaces of a finite dimensional complex vector space in terms of complex matrices thus we classify the orbits of the direct product gl m c gl m 1 r gl m 2 r acting on the set of pairs of m m t complex matrices a t t 1 2 by a 1 a 2 q p 1 p 2 qa 1 p 1 1 qa 2 p 1 2 in addition the general case of canonical forms of pairs of complex matrices is resolved

cohomology of twisted tensor products abstract it is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies we look at twisted tensor products and investigate to which extent this is still true we give an explicit description of the ext algebra of the tensor product of two modules and under certain additional conditions describe an essential part of the hochschild cohomology ring of a twisted tensor product as an application we characterize precisely when the cohomology groups over a quantum complete intersection are finitely generated over the hochschild cohomology ring moreover both for quantum complete intersections and in related cases we obtain a lower bound for the representation dimension of the algebra

on the representation dimension of finite dimensional algebras the importance of the representation finite artin algebras for the whole representation theory of artin algebras is well understood and there is much literature on the subject see 1 6 12 these are artin algebras such that every indecomposable module is finitely generated and every module is a direct sum of indecomposable modules moreover there is a bijective correspondence between the class of representation finite artin algebras and that of artin algebras with global dimension of at most 2 and with dominant dimension of at least 2 this result was established by auslander in 1 motivated by this correspondence auslander introduced the concept of representation dimension for artin algebras to study the connection of arbitrary artin algebras with representation finite artin algebras it is hoped that this notion gives a reasonable way of measuring how far an artin algebra is from being representation finite type 1 p 134 representation dimension is a morita invariant of artin algebras and its definition involves homological dimensions and modules which are both generators and cogenerators unfortunately little seems to be known about representation dimension so there are a lot of essential questions on this invariant dealing with the computation and estimation of the representation dimension of an artin algebra there are a few cases known auslander proved that the representation dimension of an artin algebra is two if and

on centrally generically tame algebras over perfect fields abstract we show that the central generic tameness of a finite dimensional algebra over a possibly finite perfect field is equivalent to its non almost sharp wildness in this case we give for each natural number d parametrizations of the indecomposable modules with central endolength d modulo finite scalar extensions over rational algebras moreover we show that the central generic tameness of is equivalent to its semigeneric tameness and that in this case algebraic boundedness coincides with central finiteness for generic modules

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

on the structure of tame graded basic hopf algebras ii abstract in this paper firstly we give a complete list of tame local graded frobenius algebras then by the method of bosonization and this list we determine the structure of tame radically graded basic hopf algebras completely

orbital stability of double solitons for the benjamin ono equation in this paper we prove the orbital stability of double solitons for the benjamin ono equation in the case of the kdv equation this stability has been proved in 17 parts of the proof given there rely on the fact that the euler lagrange equations for the conserved quantities of the kdv equation are ordinary differential equations since this is not the case for the benjamin ono equation new methods are required our approach consists in using a new invariant for multi solitons and certain new identities motivated by the sylvester law of inertia

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

the representation dimension of hecke algebras and symmetric groups abstract we establish a lower bound for the representation dimension of all the classical hecke algebras of types a b and d for all the type a algebras and most of the algebras of types b and d we also establish upper bounds moreover we establish bounds for the representation dimension of group algebras of some symmetric groups

isoinertial family of operators and convergence of kdv cnoidal waves to solitons abstract in this paper we show the convergence of korteweg de vries cnoidal waves to the limit soliton it is proved that the convergence is uniform and in h 2 norm as the period of the solutions tends to infinity families of hill operators are also studied we obtain a condition under which families of operators are isoinertial this condition is satisfied for classes of hill operators that are obtained by linearization our application is to the family of linearized operators at the kdv cnoidal waves it is proved that this family is isoinertial and also the value of the inertial index is calculated

galois actions and blocks of tame infinitesimal group schemes given an infinitesimal group that is defined over an algebraically closed field of characteristic we determine the block structure of the algebra of measures in case its principal block is tame and the height of the factor group of by its multiplicative center is at least two our results yield a complete description of the stable auslander reiten quiver of along with a criterion for the domesticity of

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

on the variational structure of breather solutions i sine gordon equation abstract in this paper we describe stability properties of the sine gordon breather solution these properties are first described by suitable variational elliptic equations which also implies that the stability problem reduces in some sense to i the study of the spectrum of explicit linear systems and ii the understanding of how bad directions if any can be controlled using low regularity conservation laws then we discuss spectral properties of a fourth order linear matrix system using numerical methods we confirm that all spectral assumptions leading to the h 2 h 1 stability of sg breathers are numerically satisfied even in the ultra relativistic singular regime

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

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

generic sheaves on elliptic curves abstract in the present paper we introduce the notion of generic sheaves on an elliptic curve e we then describe all the generic sheaves which are determined by their slopes we also show that the coherent sheaves on e can be classified by generic sheaves

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

periodic solutions of the kdv equation in this paper we construct a large family of special solutions of the kdv equation which are periodic in x and almost periodic in t these solutions lie on n dimensional tori very likely they are dense among all solutions the special solutions are characterized variationally they minimize fn u subject to the constraints fj u aj j 1 n 1 here fj denote the remarkable sequence of conserved functionals discovered by kruskal and zabusky the above minimum problem was originally suggested by them in exploring the manifold of solutions of this minimum problem we make essential use of gardner s discovery that these functionals are in involution with respect to a suitable poisson bracket gardner greene kruskal and miura have shown that the eigenvalues of the schrodinger operator are conserved functionals if the potential is a function of t and satisfies the kdv equation in section 6 a new set of conserved quantities is constructed which serve as a link between the eigenvalues of the schrodinger operator and the fj another result in section 6 is a slight sharpening of an earlier result of the author and j moser for the special solutions constructed above all but 2n 1 eigenvalues of the schrodinger operator are double the simplest class of special solutions n 1 are cnoidal waves in an appendix m hyman describes the results of computing numerically the next simplest case n 2 these calculations show that the shape of these solutions recurs exactly after a finite time in a shifted position the theory verifies this fact

sufficient conditions for stability of solitary wave solutions of model equations for long waves abstract we consider solitary wave solutions of model equations for long waves that feature a general form of linear dispersion sufficient conditions for the non linear stability of such solutions are derived these conditions are shown to obtain for the korteweg de vries equation and certain of its generalizations such as the benjamin ono equation and the intermediate long wave equation

linearized wave equation migration velocity analysis by image warping seismic imaging produces images of contrasts in physical parameters in the subsurface e g velocity or impedance to build such images a background model describing the wave kinematics in the earth is necessary in practice the structural image and background velocity model are unknown and have to be estimated from the acquired data migration velocity analysis deals with estimation of the background model in the framework of seismic migration and relies on two main elements data redundancy and invariance of the structures with respect to different seismic experiments because all the experiments probe the same model the reflectors must be invariant in suitable domains e g shots or reflection angle the semblance principle is the tool used to measure the invariance of a set of multiple images we measure the similarity of the structural features between pairs of single shot migrated images obtained from adjacent experiments by using the estimated warping vector field between two migrated images we construct an image perturbation which describes the difference in reflectivity observed by two shots we derive an expression for the image perturbation that drives a migration velocity analysis procedure based on a linearization of the wave equation with respect to the model parameters synthetic 2d examples show promising results in retrieving errors in the velocity model this methodology can be directly applied to 3d

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

migration velocity analysis using residual diffraction moveout in the poststack depth domain abstractdiffraction events contain more direct information on the medium velocity than reflection events we have developed a method for migration velocity improvement and diffraction localization based on a moveout analysis of over or undermigrated diffraction events in the depth domain the method uses an initial velocity model as input it provides an update to the velocity model and diffraction locations in the depth domain as a result the algorithm is based on the focusing of remigration trajectories from incorrectly migrated diffraction curves these trajectories are constructed by applying a ray tracing like approach to the image wave equation for velocity continuation the starting points of the trajectories are obtained from fitting an ellipse or hyperbola to the picked uncollapsed diffraction events in the depth migrated domain focusing of the remigration trajectories points out the approximate location of the associated diffractor as well as local velocity attributes apart from the migrati

lower bounds for auslander s representation dimension the notion of representation dimension of a finite dimensional algebra has been introduced by auslander he has shown that an algebra is of finite representation type if and only if its representation dimension is at most two he has expected that the representation dimension of a representation infinite algebra should measure how far this algebra is from being representation finite in many cases and thanks to iyama also in general upper bounds for the representation dimension are known however there are non trivial lower bounds only for two similarly constructed series of algebras in this thesis new lower bounds for auslander s representation dimension are constructed and more general methods are developed first we consider group algebras of elementary abelian groups we show that their representation dimension is greater than the rank of the group this leads to a proof of a conjecture of benson concerning the loewy length of blocks of group algebras then a notion of dimension of a module category is introduced this notion enables us to find better lower bounds for the representation dimension in particular it allows us for the first time to determine the value of the representation dimension of non self injective algebras of representation dimension greater than three finally we give a general criterion for finding lower bounds for auslander s representation dimension suppose there is a family of modules such that sufficiently many members of the family have certain d extensions then the representation dimension of the algebra is at least d 2 we illustrate how this criterion is applied on some interesting families of algebras it turns out that the lower bound is often the precise value of the representation dimension

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

on the normal forms of modules with respect to parametrizing bimodules abstract we present a general solution of the isomorphism and multiplicity problems restricted to the class of all modules lying in homogeneous tubes for tame algebras theorem 2 4 we introduce a notion of the characteristic polynomial of a module which plays an analogous role as in the classical situation this notion uses a smith form h b m of certain polynomial matrix h b m associated to a module m and a bimodule b parametrizing a family of homogeneous modules f we show that h b m encodes an essential information on a decomposition of m into a direct sum of indecomposables from f theorem 2 2 theorem 2 3

characterizations of algebras with small homological dimensions abstract we introduce the class of double tilted algebras containing the class of tilted algebras and prove various characterizations in particular we show that the class of double tilted algebras is the class of all artin algebras whose ar quiver admits a faithful double section with a natural property moreover we prove that the class of double tilted algebras coincides with the class of all artin algebras of global dimension three for which every indecomposable finitely generated module has projective or injective dimension at most one we also describe the structure of the category of finitely generated modules as well as the ar quiver of double tilted algebras

minimum entropy deconvolution with frequency domain constraints a method for reconstructing the reflectivity spectrum using the minimum entropy criterion is presented the algorithm fmed described is compared with the classical minimum entropy deconvolution med as well as with the linear programming lp and autoregressive ar approaches the med is performed by maximizing an entropy norm with respect to the coefficients of a linear operator that deconvolves the seismic trace by comparison the approach presented here maximizes the norm with respect to the missing frequencies of the reflectivity series spectrum this procedure reduces to a nonlinear algorithm that is able to carry out the deconvolution of band limited data avoiding the inherent limitations of linear operators the proposed method is illustrated under a variety of synthetic examples field data are also used to test the algorithm the results show that the proposed method is an effective way to process band limited data the fmed and the lp arise from similar conceptions both methods seek an extremum of a particular norm subjected to frequency constraints in the lp approach the linear programming problem is solved using an adaptation of the simplex method which is a very expensive procedure the fmed uses only two fast fourier transforms ffts per iteration hence the computational cost of the inversion is reduced

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

the green correspondence for the representations of hecke algebras of type ᵣ we first prove the conjecture mentioned by leonard k jones in his thesis by applying this conjecture we obtain that the vertex of an indecomposable xf module is an i parabolic subgroup finally we establish the green correspondence for the representations of hecke algebras of type ar

almost split sequences for complexes of fixed size abstract let a be an additive k category k a commutative artinian ring and n 1 we denote by c n a the category of complexes x x i d x i i z in a with x i 0 if i 1 n we see that c n a is endowed with a natural exact structure and its global dimension is at most n 1 in case a is a dualizing category we prove that c n a has almost split sequences in the sense of p draxler i reiten s o smalo o solberg exact categories and vector space categories with an appendix by b keller trans amer math soc 351 2 1999 647 682 or r bautista the category of morphisms between projective modules comm algebra 32 11 2004 4303 4331 if a is the category of finitely generated projective modules an artin algebra we prove that the ends of an almost split sequence are related by an auslander reiten translation functor which is defined in the most general category c n proj

the structure and homological properties of generalized standard auslander reiten components abstract we describe the structure and homological properties of arbitrary generalized standard auslander reiten components of artin algebras in particular we prove that for all but finitely many indecomposable modules in such components the euler characteristic is defined and nonnegative further we provide a handy criterion for an infinite auslander reiten component of an artin algebra to be generalized standard we solve also the long standing open problem concerning the structure of artin algebras admitting a separating family of auslander reiten components