共查询到20条相似文献,搜索用时 15 毫秒
1.
Karin Erdmann 《Journal of Pure and Applied Algebra》2011,215(2):185-200
One of our main results is a classification of all the weakly symmetric radical cube zero finite dimensional algebras over an algebraically closed field having a theory of support via the Hochschild cohomology ring satisfying Dade’s Lemma. In the process we give a characterization of when a finite dimensional Koszul algebra has such a theory of support in terms of the graded centre of the Koszul dual. 相似文献
2.
Alex S. Dugas 《Journal of Pure and Applied Algebra》2010,214(6):990-170
We say that an algebra A is periodic if it has a periodic projective resolution as an (A,A)-bimodule. We show that any self-injective algebra of finite representation type is periodic. To prove this, we first apply the theory of smash products to show that for a finite Galois covering B→A, B is periodic if and only if A is. In addition, when A has finite representation type, we build upon results of Buchweitz to show that periodicity passes between A and its stable Auslander algebra. Finally, we use Asashiba’s classification of the derived equivalence classes of self-injective algebras of finite type to compute bounds for the periods of these algebras, and give an application to stable Calabi-Yau dimensions. 相似文献
3.
Claus Michael Ringel 《Journal of Pure and Applied Algebra》2010,214(9):1687-1692
Let Λ be an artin algebra and X a finitely generated Λ-module. Iyama has shown that there exists a module Y such that the endomorphism ring Γ of X⊕Y is quasi-hereditary, with a heredity chain of length n, and that the global dimension of Γ is bounded by this n. In general, one only knows that a quasi-hereditary algebra with a heredity chain of length n must have global dimension at most 2n−2. We want to show that Iyama’s better bound is related to the fact that the ring Γ he constructs is not only quasi-hereditary, but even left strongly quasi-hereditary. By definition, the left strongly quasi-hereditary algebras are the quasi-hereditary algebras with all standard left modules of projective dimension at most 1. 相似文献
4.
Roberto Martinéz-Villa 《Journal of Pure and Applied Algebra》2011,215(4):546-565
Motivated by constructions in the representation theory of finite dimensional algebras we generalize the notion of Artin-Schelter regular algebras of dimension n to algebras and categories to include Auslander algebras and a graded analogue for infinite representation type. A generalized Artin-Schelter regular algebra or a category of dimension n is shown to have common properties with the classical Artin-Schelter regular algebras. In particular, when they admit a duality, then they satisfy Serre duality formulas and the -category of nice sets of simple objects of maximal projective dimension n is a finite length Frobenius category. 相似文献
5.
Suppose k is a field. Let A and B be two finite dimensional k-algebras such that there is a stable equivalence of Morita type between A and B. In this paper, we prove that (1) if A and B are representation-finite then their Auslander algebras are stably equivalent of Morita type; (2) The n-th Hochschild homology groups of A and B are isomorphic for all n≥1. A new proof is also provided for Hochschild cohomology groups of self-injective algebras under a stable equivalence of Morita type. 相似文献
6.
7.
We introduce and study the class of weighted locally gentle quivers. This naturally extends the class of gentle quivers and gentle algebras, which have been intensively studied in the representation theory of finite-dimensional algebras, to a wider class of potentially infinite-dimensional algebras. Weights on the arrows of these quivers lead to gradings on the corresponding algebras. For natural grading by path lengths, any locally gentle algebra is Koszul. The class of locally gentle algebras consists of the gentle algebras together with their Koszul duals.Our main result is a general combinatorial formula for the determinant of the weighted Cartan matrix of a weighted locally gentle quiver. We show that this weighted Cartan determinant is a rational function which is completely determined by the combinatorics of the quiver-more precisely by the number and the weight of certain oriented cycles. 相似文献
8.
9.
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. 相似文献
10.
Thorsten Holm 《Archiv der Mathematik》2005,85(3):233-239
The determinant of the Cartan matrix of a finite dimensional algebra is an invariant of the derived category and can be very helpful for derived equivalence classifications. In this paper we determine the determinants of the Cartan matrices for all gentle algebras. This is a class of algebras of tame representation type which occurs naturally in various places in representation theory. The definition of these algebras is of a purely combinatorial nature, and so are our formulae for the Cartan determinants.Received: 29 October 2004 相似文献
11.
Summary Given a sequence of ϕ-mixing random variables not necessarily stationary, a Chernoff-Savage theorem for two-sample linear
rank statistics is proved using the Pyke-Shorack [5] approach based on weak convergence properties of empirical processes
in an extended metric. This result is a generalization of Fears and Mehra [4] in that the stationarity is not required and
that the condition imposed on the mixing numbers is substantially relaxed. A similar result is shown to hold for strong mixing
sequences under slightly stronger conditions on the mixing numbers.
Research partially supported by the National Research Council of Canada under Grant No. A-3954. 相似文献
12.
《Quaestiones Mathematicae》2013,36(3):465-474
Abstract This paper surveys a selection of results in the literature on torsion preradicals; these are left exact preradical functors on the category of unital right modules over an associative ring with identity. Various well known classes of rings such as semisimple, artinian, perfect and strongly prime are characterized in terms of torsion preradicals. A classification of prime rings using torsion preradicals is also exhibited. Rings all of whose torsion preradicals are radicals and rings whose torsion preradicals commute, are investigated. An application of the latter condition to Jacobson's Conjecture is presented. 相似文献
13.
The well-known list of Happel-Vossieck of tame concealed algebras in terms of quivers with relations, and the list of A. Seven of minimal infinite cluster quivers are compared. There is a 1-1 correspondence between the items in these lists, and we explain how an item in one list naturally corresponds to an item in the other list. A central tool for understanding this correspondence is the theory of cluster-tilted algebras. 相似文献
14.
Certain classes of lean quasi-hereditary algebras play a central role in the representation theory of semisimple complex Lie
algebras and algebraic groups. The concept of a lean semiprimary ring, introduced recently in [1] is given here a homological
characterization in terms of the surjectivity of certain induced maps between Ext1-groups. A stronger condition requiring the surjectivity of the induced maps between Ext
k
-groups for allk≥1, which appears in the recent work of Cline, Parshall and Scott on Kazhdan-Lusztig theory, is shown to hold for a large
class of lean quasi-hereditary algebras.
Research partially supported by NSERC of Canada and by Hungarian National Foundation for Scientific Research grant no. 1903
Research partially supported by NSERC of Canada 相似文献
15.
J. Kurdics 《Periodica Mathematica Hungarica》1996,32(1-2):57-64
We characterize the group algebras of finite groups over a field of characteristic 2 with metabelian groups of units.Dedicated to Professor László Fuchs on his 70th birthdayResearch was supported by Hungarian National Fund for Scientific Research grant No. T014279 相似文献
16.
We prove that the class of finite dimensional selfinjective algebras over a field which admit Galois coverings by the repetitive
algebras of the quasitilted algebras, with Galois groups generated by compositions of the Nakayama automorphisms with strictly
positive automorphisms, is invariant under stable and derived equivalences.
Dedicated to Claus Michael Ringel on the occasion of his sixtieth birthday 相似文献
17.
Calin Chindris 《Journal of Pure and Applied Algebra》2009,213(7):1418-1429
We show that a finite, connected quiver Q without oriented cycles is a Dynkin or Euclidean quiver if and only if all orbit semigroups of representations of Q are saturated. 相似文献
18.
Miles Holloway 《Archiv der Mathematik》2008,90(4):311-316
We answer a question raised in [9] by showing the equality of two different definitions of rank variety for finitely generated
modules over truncated polynomial algebras. We do this by establishing an isomorphism of algebras used in the two definitions
of rank variety.
Received: 23 April 2007 相似文献
19.
Pu Zhang 《Advances in Mathematics》2004,183(1):80-126
By introducing a twisted Hopf algebra we unify several important objects of study. Skew derivations of such an algebra are defined and the corresponding skew differential operator algebras are studied. This generalizes results in the Weyl algebra. Applying this investigation to the twisted Ringel-Hall algebra we get, in particular, a natural realization of the non-positive part of a quantized generalized Kac-Moody algebra, by identifying the canonical generators with some linear, skew differential operators. This also induces some algebras which are quantum-group like. 相似文献
20.
We study self-extensions of modules over symmetric artin algebras. We show that non-projective modules with eventually vanishing self-extensions must lie in AR components of stable type ZA∞. Moreover, the degree of the highest non-vanishing self-extension of these modules is determined by their quasilength. This has implications for the Auslander–Reiten Conjecture and the Extension Conjecture. 相似文献