共查询到20条相似文献,搜索用时 31 毫秒
1.
Kenji Nishida 《Algebras and Representation Theory》2006,9(1):13-31
We generalize results of Foxby concerning a commutative Nötherian ring to a certain noncommutative Nötherian algebra Λ over a commutative Gorenstein complete local ring. We assume that Λ is a Cohen–Macaulay isolated singularity having a dualizing module. Then the same method as in the commutative cases works and we obtain a category equivalence between two subcategories of mod Λ, one of which includes all finitely generated modules of finite Gorenstein dimension. We give examples of such algebras which are not Gorenstien; orders related to almost Bass orders and some k-Gorenstein algebras for an integer k.Presented by I. Reiten
★The author is supported by Grant-in-Aid for Scientific Researches B(1) No. 14340007 in Japan. 相似文献
2.
In this paper, we discuss the representation-finite selfinjective artin algebras of classB
n andC
n and obtain the following main results:
For any fieldk, let Λ be a representation-finite selfinjective artin algebras of classB
n orC
n overk.
相似文献
(a) | We give the configuration ofZB n andZC n. |
(b) | We show that Λ is standard. |
(c) | Under the condition ofk being a perfect field, we describe Λ by boundenk-species and show that Λ is a finite covering of the trivial extension of some tilted algebra of typeB n orC n. |
3.
It is shown that an algebra Λ can be lifted with nilpotent Jacobson radical r = r(Λ) and has a generalized matrix unit {e
ii
}
I
with each ē
ii
in the center of if Λ is isomorphic to a generalized path algebra with weak relations. Representations of the generalized path algebras are given.
As a corollary, Λ is a finite algebra with non-zero unity element over a perfect field k (e.g., a field with characteristic zero or a finite field) if Λ is isomorphic to a generalized path algebra k (D, Ω, ρ) of finite directed graph with weak relations and dim < ∞; Λ is a generalized elementary algebra which can be lifted with nilpotent Jacobson radical and has a complete set of pairwise
orthogonal idempotents if Λ is isomorphic to a path algebra with relations.
Presented by Idun Reiten. 相似文献
4.
To obtain the representation (L, R) of Lie algebras over the ring Λ, we construct the lattice of subrepresentations ℒ(L, R). Relations between the algebras L and R and the lattice ℒ(L, R) are studied. It turns out that in some cases the isomorphism of the lattice ℒ(L, R) can be continued so as to obtain a wider sublattice ℒ(LλR) consisting of subalgebras of a semidirect product LλR.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 46, Algebra,
2007. 相似文献
5.
Let k(x) be the field of fractions of the polynomial algebra k[x] over the field k. We prove that, for an arbitrary finite dimensional k-algebra Λ, any finitely generated Λ ⊗k k(x)-module M such that its minimal projective presentation admits no non-trivial selfextension is of the form M ≅ Nk(x), for some finitely generated Λ-module N. Some consequences are derived for tilting modules over the rational algebra Λ ⊗k k(x) and for some generic modules for Λ.
Received: 24 November 2003; revised: 11 February 2005 相似文献
6.
《代数通讯》2013,41(4):1837-1858
Abstract We present “canonical forms” of finite dimensional (quasi-Frobenius) commutative algebras Λ over a field k such that the radical cubed is zero and Λ modulo the radical is a product of copies of k. We also determine the isomorphism classes of the algebras Λ over some typical fields. 相似文献
7.
8.
We consider the algebras Λ which satisfy the property that for each indecomposable module X, either its projective dimension pdΛ
X is at most one or its injective dimension idΛ
X is at most one. This clearly generalizes the so-called quasitilted algebras introduced by Happel–Reiten–Smal?. We show that
some of the niciest features for this latter class of algebras can be generalized to the case we are considering, in particular
the existence of a trisection in its module category.
Received: 26 August 1998 相似文献
9.
Let Λ be a Fibonacci algebra over a field k. The multiplication of Hochschild cohomology ring of Λ induced by the Yoneda product is described explicitly. As a consequence,
the multiplicative structure of Hochschild cohomology ring of Λ is proved to be trivial. 相似文献
10.
Let Λ be a finite-dimensional algebra over an algebraically closed field k. We denote by mod Λ the category of finitely generated left Λ-modules. Consider the family ℱ(u) of the indecomposables M∈mod Λ such that
, where
is the subspace of morphisms which factorize through semisimple modules. If P,Q are projectives in mod Λ, ℱ(u)(P,Q) is the family of those modules M∈ℱ(u) such that a minimal projective presentation is of the formfM: P→Q. We prove that if Λ is of tame representation type then each ℱ(P,Q) has only a finite number of isomorphism classes or is parametrized by μ(u,P,Q) one-parameter families. We give an upper bound for this number in terms of u,P and Q. Then we give some sufficient conditions for tame of polynomial growth type. For the proof we consider similar results for
bocses.
Presented by Y. Drozd
Mathematics Subject Classifications (2000) 16G60, 16G70, 16G20. 相似文献
11.
Otmar Venjakob 《Journal of the European Mathematical Society》2002,4(3):271-311
This paper is motivated by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa
algebra, i.e. the completed group algebra, Λ of a p-adic analytic group G. For G without any p-torsion element we prove that Λ is an Auslander regular ring. This result enables us to give a good definition of the notion
of a pseudo-nullΛ-module. This is classical when G=ℤ
k
p
for some integer k≥1, but was previously unknown in the non-commutative case. Then the category of Λ-modules up to pseudo-isomorphisms is studied
and we obtain a weak structure theorem for the ℤ
p
-torsion part of a finitely generated Λ-module. We also prove a local duality theorem and a version of Auslander-Buchsbaum
equality. The arithmetic applications to the Iwasawa theory of abelian varieties are published elsewhere.
Received May 12, 2001 / final version received July 5, 2001?Published online September 3, 2001 相似文献
12.
Michael Natapov 《Israel Journal of Mathematics》2008,164(1):61-73
Let G be a finite group and let k be a field. We say that G is a projective basis of a k-algebra A if it is isomorphic to a twisted group algebra k
α
G for some α ∈ H
2(G, k
×), where the action of G on k
× is trivial. In a preceding paper by Aljadeff, Haile and the author it was shown that if a group G is a projective basis of a k-central division algebra, then G is nilpotent and every Sylow p-subgroup of G is on the short list of p-groups, denoted by Λ. In this paper we complete the classification of projective bases of division algebras by showing that
every group on that list is a projective basis for a suitable division algebra.
We also consider the question of uniqueness of a projective basis of a k-central division algebra. We show that basically all groups on the list Λ but one satisfy certain rigidity property.
This work was supported in part by the US-Israel Binational Science Foundation Grant 82334. The author would like to thank
Louis Rowen and the Department Department of Mathematics at Bar Ilan University, Ramat Gan, Israel, for kind hospitality and
support. 相似文献
13.
Let k be an algebraically closed field. Let Λ be the path algebra over k of the linearly oriented quiver
\mathbb An\mathbb A_n for n ≥ 3. For r ≥ 2 and n > r we consider the finite dimensional k −algebra Λ(n,r) which is defined as the quotient algebra of Λ by the two sided ideal generated by all paths of length r. We will determine for which pairs (n,r) the algebra Λ(n,r) is piecewise hereditary, so the bounded derived category D
b
(Λ(n,r)) is equivalent to the bounded derived category of a hereditary abelian category H\mathcal H as triangulated category. 相似文献
14.
A number of combinatorial problems are treated using properties of abelian null-square-generated and idempotent-generated
subalgebras of Clifford algebras. For example, the problem of deciding whether or not a graph contains a Hamiltonian cycle
is known to be NP-complete. By considering entries of Λk, where Λ is an appropriate nilpotent adjacency matrix, the k-cycles in any finite graph are recovered. Within the algebra context (i.e., considering the number of multiplications performed
within the algebra), these problems are reduced to matrix multiplication, which is in complexity class P. The Hamiltonian
cycle problem is one of many problems moved from classes NP-complete and #P-complete to class P in this context. Other problems
considered include the set covering problem, counting the edge-disjoint cycle decompositions of a finite graph, computing
the permanent of an arbitrary matrix, computing the girth and circumference of a graph, and finding the longest path in a
graph. 相似文献
15.
BinodChandraTripathy SabitaMahanta 《应用数学学报(英文版)》2004,20(3):487-494
In this article we introduce the vector valued sequence space m(E_k,φ,∧),associated with themultiplier sequence ∧=(λ_k) of non-zero complex numbers,and the terms of the sequence are chosen from theseminormed spaces E_k,seminormed by f_k for all k∈N.This generalizes the sequence space m(φ) introducedand studied by Sargent.We study some of its properties like solidity,completeness,and obtain some inclusionresults.We also characterize the multiplier problem and obtain the corresponding spaces dual to m(E_k,φ,∧).We prove some general results too. 相似文献
16.
Zhao Yong HUANG 《数学学报(英文版)》2007,23(8):1463-1474
Let A and F be artin algebras and ∧UГa paper, we first introduce the notion of k-Gorenstein faithfully balanced selforthogonal bimodule. In this modules with respect to ∧UГ and then characterize it in terms of the U-resolution dimension of some special injective modules and the property of the functors Ext^i (Ext^i (-, U), U) preserving monomorphisms, which develops a classical result of Auslander. As an application, we study the properties of dual modules relative to Gorenstein bimodules. In addition, we give some properties of ∧UГwith finite left or right injective dimension. 相似文献
17.
It is well-known that for a lattice-finite order Λ over a complete discrete valuation domain, the radical of Λ-lat (the category of Λ-lattices) is nilpotent modulo projectives. Iyama has shown that this property merely depends on the combinatorial
data given by the Auslander–Reiten quiver of Λ. Moreover, he established a criterion for a finite (symmetrizable) translation
quiver Q to be the Auslander–Reiten quivers of an order Λ. We improve his characterization by showing that the remaining conditions
on Q can be replaced by the existence of an additive function on the vertices of Q (Theorem 4). Our proof rests on a functorial theory of ladders, expressing the Auslander–Reiten structure of Λ-lat by means of an adjoint pair of functors L⊣L− in the homotopy category of two-termed complexes over Λ-lat.
Presented by I. Reiten
Mathematics Subject Classifications (2000) Primary: 16G70, 16G30; secondary: 16G60. 相似文献
18.
D. V. Millionshchikov 《Proceedings of the Steklov Institute of Mathematics》2008,263(1):99-111
We compute explicitly the adjoint cohomology of two ℕ-graded Lie algebras of maximal class (infinite-dimensional filiform
Lie algebras) m0 and m2. It is known that up to an isomorphism there are only three ℕ-graded Lie algebras of maximal class. The third algebra from
this list is the “positive” part L
1 of the Witt (or Virasoro) algebra, and its adjoint cohomology was computed earlier by Feigin and Fuchs.
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Vol. 263, pp. 106–119. 相似文献
19.
ZHU Bin Department of Mathematical Sciences Tsinghua University Beijing China 《中国科学A辑(英文版)》2006,49(12):1839-1854
Given a symmetrizable generalized Cartan matrix A, for any index k, one can define an automorphism associated with A, of the field Q(u1,…, un) of rational functions of n independent indeterminates u1,…,un.It is an isomorphism between two cluster algebras associated to the matrix A (see sec. 4 for the precise meaning). When A is of finite type, these isomorphisms behave nicely; they are compatible with the BGP-reflection functors of cluster categories defined in a previous work if we identify the indecomposable objects in the categories with cluster variables of the corresponding cluster algebras, and they are also compatible with the "truncated simple reflections" defined by Fomin-Zelevinsky. Using the construction of preprojective or preinjective modules of hereditary algebras by DIab-Ringel and the Coxeter automorphisms (i.e. a product of these isomorphisms), we construct infinitely many cluster variables for cluster algebras of infinite type and all cluster variables for finite types. 相似文献
20.
Let ∧ be the Z2-Galois covering of the Grassmann algebra A over a field k of characteristic not equal to 2. In this paper, the dimensional formulae of Hochschild homology and cohomology groups of ∧ are calculated explicitly. And the cyclic homology of∧ can also be calculated when the underlying field is of characteristic zero. As a result, we prove that there is an isomorphism from i≥1 HH^i(∧) to i≥1 HH^i(∧). 相似文献