共查询到20条相似文献,搜索用时 0 毫秒
1.
Ibrahim Assem 《代数通讯》2013,41(12):4711-4721
We prove that indecomposable transjective modules over cluster-tilted algebras are uniquely determined by their dimension vectors. Similarly, we prove that for cluster-concealed algebras, rigid modules lifting to rigid objects in the corresponding cluster category are uniquely determined by their dimension vectors. Finally, we apply our results to a conjecture of Fomin and Zelevinsky on denominators of cluster variables. 相似文献
2.
3.
Let H be a hereditary algebra of Dynkin type D n over a field k and 𝒞 H be the cluster category of H. Assume that n ≥ 5 and that T and T′ are tilting objects in 𝒞 H . We prove that the cluster-tilted algebra Γ = End𝒞 H (T)op is isomorphic to Γ′ = End𝒞 H (T′)op if and only if T = τ i T′ or T = στ j T′ for some integers i and j, where τ is the Auslander–Reiten translation and σ is the automorphism of 𝒞 H defined in Section 4. 相似文献
4.
Ayako Itaba 《代数通讯》2013,41(1):404-415
We calculate the dimensions of the Hochschild cohomology groups of a self-injective special biserial algebra Λ s obtained by a circular quiver with double arrows. Moreover, we give a presentation of the Hochschild cohomology ring modulo nilpotence of Λ s by generators and relations. This result shows that the Hochschild cohomology ring modulo nilpotence of Λ s is finitely generated as an algebra. 相似文献
5.
Let k be a fixed algebraically closed field of arbitrary characteristic,let Λ be a finite dimensional self-injective k-algebra,and let V be an indecomposable non-projective left Λ-module with finite dimension over k.We prove that if τΛV is the Auslander-Reiten translation of V,then the versal deformation rings R(Λ,V)and R(Λ,τΛV)(in the sense of F.M.Bleher and the second author)are isomorphic.We use this to prove that if Λ is further a cluster-tilted k-algebra,then R(Λ,V)is universal and isomorphic to k. 相似文献
6.
HAN Guo-qiang YA O Hai-lou 《数学季刊》2014,(2):244-246
Let K be an algebraically closed field and A be a finite dimensional algebra over K. In this paper we give a classification of biserial incidence algebras with quiver methods. 相似文献
7.
Claus Michael Ringel 《Archiv der Mathematik》2008,91(3):218-225
We are going to determine the self-injective cluster-tilted algebras. All are of finite representation type and special biserial.
There are two different classes. The first class are the self-injective serial (or Nakayama) algebras with n ≥ 3 simple modules and Loewy length n–1. The second class of algebras has an even number 2m of simple modules; m indecomposable projective modules have length 3, the remaining m have length m + 1.
Received: 28 May 2007 相似文献
8.
By an algebra we mean an associative k-algebra with identity,where k is an algebraically closed field. All algebras are assumedto be finite dimensional over k (except the path algebra kQ).An algebra is said to be biserial if every indecomposable projectiveleft or right -module P contains uniserial submodules U andV such that U+V=Rad(P) and UV is either zero or simple. (Recallthat a module is uniserial if it has a unique composition series,and the radical Rad(M) of a module M is the intersection ofits maximal submodules.) Biserial algebras arose as a naturalgeneralization of Nakayama's generalized uniserial algebras[2]. The condition first appeared in the work of Tachikawa [6,Proposition 2.7], and it was formalized by Fuller [1]. Examplesinclude blocks of group algebras with cyclic defect group; finitedimensional quotients of the algebras (1)(4) and (7)(9)in Ringel's list of tame local algebras [4]; the special biserialalgebras of [5, 8] and the regularly biserial algebras of [3].An algebra is basic if /Rad() is a product of copies of k.This paper contains a natural alternative characterization ofbasic biserial algebras, the concept of a bisected presentation.Using this characterization we can prove a number of resultsabout biserial algebras which were inaccessible before. In particularwe can describe basic biserial algebras by means of quiverswith relations. 相似文献
9.
10.
T. Skrypnyk 《Acta Appl Math》2007,99(3):261-282
We construct a family of special quasigraded Lie algebras
of functions of one complex variables with values in finite-dimensional Lie algebra
, labeled by the special 2-cocycles F on
. The main property of the constructed Lie algebras
is that they admit Kostant-Adler-Symes scheme. Using them we obtain new integrable finite-dimensional Hamiltonian systems
and new hierarchies of soliton equations. 相似文献
11.
Changjian Fu 《Algebras and Representation Theory》2014,17(4):1137-1143
We show the existence of Hall polynomials for representation-finite repetitive cluster-tilted algebras. 相似文献
12.
13.
14.
15.
Thomas Cassidy 《代数通讯》2013,41(9):3742-3752
Vatne [13] and Green and Marcos [9] have independently studied the Koszul-like homological properties of graded algebras that have defining relations in degree 2 and exactly one other degree. We contrast these two approaches, answer two questions posed by Green and Marcos, and find conditions that imply the corresponding Yoneda algebras are generated in the lowest possible degrees. 相似文献
16.
In a previous paper, the first-named author introduced generalized structurable algebras, while the second-named author introduced the isotopies of Lie algebras. In this paper, we combine the two analyses, submit the notion of isogeneralized structural algebras, and show that they include Lie algebras, all their axiom-preserving generalizations of graded, supersymmetric or isotopic type, as well as numerous other algebras. 相似文献
17.
《代数通讯》2013,41(4):1765-1775
Abstract This paper studies two homogenizations of the down-up algebras introduced in Benkart and Roby (Benkart, G., Roby, T. (1998). Down-up Algebras. J. Algebra 209:305–344). We show that in all cases the homogenizing variable is not a zero-divisor, and that when the parameter β is non-zero, the homogenized down-up algebra is a Noetherian domain and a maximal order, and also Artin-Schelter regular, Auslander regular, and Cohen-Macaulay. We show that all homogenized down-up algebras have global dimension 4 and Gelfand-Kirillov dimension 4, and with one exception all homogenized down-up algebras are prime rings. We also exhibit a basis for homogenized down-up algebras and provide a necessary condition for a Noetherian homogenized down-up algebra to be a Hopf algebra. 相似文献
18.
19.
Marina V. Tvalavadze 《代数通讯》2013,41(8):2816-2837
We study the universal enveloping algebras of the one-parameter family of solvable 5-dimensional non-Lie Malcev algebras. We explicitly determine the universal nonassociative enveloping algebras (in the sense of Pérez-Izquierdo and Shestakov) and the centers of the universal enveloping algebras. We also determine the universal alternative enveloping algebras. 相似文献
20.
Let L be a Lie algebra with universal enveloping algebra U(L). We prove that if H is another Lie algebra with the property that U(L) ≅ U(H) then certain invariants of L are inherited by H. For example, we prove that if L is nilpotent then H is nilpotent with the same class as L. We also prove that if L is nilpotent of class at most two then L is isomorphic to H.
Presented by D. Passman 相似文献