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1.
Yao Hailou 《数学季刊》1998,(3)
§1. IntroductionLetAbeanartinalgebra,modAbethecategoryoffinitelygeneratedrightA-modules,ΓAbeitsAuslander-Reitenquiver,thenthereisanonzeromapbetweenanytwonon-isomorphicmodulesinmodAifandonlyifthereisapathbetweenthetwoverticescorrespondingtothesetwomod… 相似文献
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Kenta Ueyama 《代数通讯》2013,41(10):4253-4268
The purpose of this paper is to connect the notion of Gorenstein dimension with AS-Gorenstein algebras. In particular, we show that a noetherian connected graded algebra having a balanced dualizing complex is AS-Gorenstein if the balanced dualizing complex has finite Gorenstein dimension. As a preparation, we generalize the Auslander–Bridger formula to the class of noncommutative noetherian connected graded algebras having balanced dualizing complexes. 相似文献
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Karin Erdmann Miles Holloway Rachel Taillefer Nicole Snashall Øyvind Solberg 《K-Theory》2004,33(1):67-87
Support varieties for any finite dimensional algebra over a field were introduced in (Proc. London Math. Soc. 88 (3) (2004) 705–732) using graded subalgebras of the Hochschild cohomology ring. We mainly study these varieties for selfinjective algebras under appropriate finite generation hypotheses. Then many of the standard results from the theory of support varieties for finite groups generalize to this situation. In particular, the complexity of the module equals the dimension of its corresponding variety, all closed homogeneous varieties occur as the variety of some module, the variety of an indecomposable module is connected, the variety of periodic modules are lines and for symmetric algebras a generalization of Webbs theorem is true. As a corollary of a more general result we show that Webbs theorem generalizes to finite dimensional cocommutative Hopf algebras.Received November 2003Mathematics Subject Classifications (2000) Primary: 16E40, 16G10, 16P10, 16P20; Secondary: 16G70. 相似文献
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We show that if A is a representation-finite selfinjective Artin algebra, then every P ? ? K b(𝒫 A ) with Hom K(Mod?A)(P ?,P ?[i]) = 0 for i ≠ 0 and add(P ?) = add(νP ?) is a direct summand of a tilting complex, and that if A, B are derived equivalent representation-finite selfinjective Artin algebras, then there exists a sequence of selfinjective Artin algebras A = B 0, B 1,…, B m = B such that, for any 0 ≤ i < m, B i+1 is the endomorphism algebra of a tilting complex for B i of length ≤ 1. 相似文献
5.
Osamu Iyama 《Advances in Mathematics》2011,226(1):1
The concept of cluster tilting gives a higher analogue of classical Auslander correspondence between representation-finite algebras and Auslander algebras. The n-Auslander–Reiten translation functor τn plays an important role in the study of n-cluster tilting subcategories. We study the category Mn of preinjective-like modules obtained by applying τn to injective modules repeatedly. We call a finite-dimensional algebra Λ n-complete if for an n-cluster tilting object M. Our main result asserts that the endomorphism algebra EndΛ(M) is (n+1)-complete. This gives an inductive construction of n-complete algebras. For example, any representation-finite hereditary algebra Λ(1) is 1-complete. Hence the Auslander algebra Λ(2) of Λ(1) is 2-complete. Moreover, for any n?1, we have an n-complete algebra Λ(n) which has an n-cluster tilting object M(n) such that Λ(n+1)=EndΛ(n)(M(n)). We give the presentation of Λ(n) by a quiver with relations. We apply our results to construct n-cluster tilting subcategories of derived categories of n-complete algebras. 相似文献
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Let A and B be Artin R-algebras of finite Cohen-Macaulay type. Then we prove that, if A and B are standard derived equivalent, then their Cohen-Macaulay Auslander algebras are also derived equivalent. And we show that Gorenstein projective conjecture is an invariant under standard derived equivalence between Artin R-algebras. 相似文献
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Rafał Bocian 《代数通讯》2013,41(12):4235-4257
We classify all selfinjective finite dimensional algebras over an algebraically closed field which are socle equivalent to the selfinjective algebras of Euclidean type. In particular, nonstandard domestic selfinjective algebras in any characteristic of the base field are exhibited. 相似文献
10.
In this paper we study Auslander-Reiten sequences of modules with finite complexity over selfinjective artin algebras. In
particular, we show that for all eventually Ω-perfect modules of finite complexity, the number of indecomposable non projective
summands of the middle term of such sequences is bounded by 4. We also describe situations in which all non projective modules
in a connected component of the Auslander-Reiten quiver are eventually Ω-perfect. 相似文献
11.
We prove new results on the stable equivalences of selfinjective Artin algebras of tilted Dynkin type, extending the main results of Skowroński and Yamagata to arbitrary tilted type.Presented by I. Reiten 相似文献
12.
Grzegorz Bobiński 《代数通讯》2013,41(6):2219-2234
Let 𝒜 = (A 1, A 12, A 2) be a locally D 8 amalgam with a finite completion G. Suppose that A 1 ∈ Syl 2(G) and N A 1 (A 12) is Abelian. We determine G/O(G). 相似文献
13.
多尺度分析生成元的刻画 总被引:1,自引:0,他引:1
本文将给出多尺度分析生成元的一种完全刻画.将证明:函数φ∈L~2(R)是二进多尺度分析生成元的充要条件是(1)存在{a_k}∈l~2,φ(x)=∑_(k∈Z)a_kφ(2x-k);(2)存在正数A相似文献
14.
Andrea Jedwab 《代数通讯》2013,41(9):3456-3468
We introduce an invariant for the irreducible representations of finite dimensional Hopf algebras, defined as the trace of a map induced by the antipode on the endomorphisms of each corresponding simple module. We also compute the value of this invariant for the representations of two families of non-semisimple Hopf algebras. 相似文献
15.
We give a complete derived equivalence classification of all nonstandard representation-infinite domestic selfinjective algebras over an algebraically closed field. As a consequence, a complete stable equivalence classification of these algebras is obtained. 相似文献
16.
We provide a characterization for the endomorphism algebra of a generator to be a Morita algebra. As an application, n-Auslander algebras which are Morita algebras simultaneously are characterized. 相似文献
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Using Grothendieck's semicontinuity theorem for half-exact functors,we derive two semicontinuity results on Hochschild cohomology.We apply these to show that the first Hochschild cohomogy groupof the mesh algebra of a translation quiver over a domain vanishesif and only if the translation quiver is simply connected. Wethen establish an exact sequence relating the first Hochschildcohomology group of an algebra to that of the endomorphism algebraof a module and apply it to study the first Hochschild cohomologygroup of an Auslander algebra. Our main result shows that fora finite-dimensional and representation-finite algebra algebraA over an algebraically closed field with Auslander algebra the following conditions are equivalent:
- (1)A admits no outer derivation;
- (2) admits no outer derivations;
- (3) A is simply connected;
- (4) is strongly simply connected.
20.
Alicja Jaworska 《代数通讯》2013,41(11):3935-3947
There are considered trivial extensions of minimal 2-fundamental algebras. It is shown that if the Auslander–Reiten quiver Γ A of a minimal 2-fundamental algebra A contains a starting component or an ending component which is not generalized standard, then the Auslander–Reiten quiver Γ T(A) of the trivial extension T(A) of A contains also a component that is not a generalized standard. 相似文献