On stable equivalences of Morita type for finite dimensional algebras
نویسندگان
چکیده
منابع مشابه
On Stable Equivalences of Morita Type for Finite Dimensional Algebras
In this paper, we assume that algebras are finite dimensional algebras with 1 over a fixed field k and modules over an algebra are finitely generated left unitary modules. Let A and B be two algebras (where k is a splitting field for A and B) with no semisimple summands. If two bimodules AMB and BNA induce a stable equivalence of Morita type between A and B, and if N⊗A− maps any simple A-module...
متن کاملConstruction of Stable Equivalences of Morita Type for Finite-dimensional Algebras I
In the representation theory of finite groups, the stable equivalence of Morita type plays an important role. For general finite-dimensional algebras, this notion is still of particular interest. However, except for the class of self-injective algebras, one does not know much on the existence of such equivalences between two finite-dimensional algebras; in fact, even a nontrivial example is not...
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Throughout this paper k denotes an algebraically closed field, and all algebras considered here are assumed to be basic, connected, finite-dimensional k-algebras with identity. For an algebra Λ, we denote by modΛ and by modΛ the category of finitedimensional (right) Λ-modules and its stable category, respectively. Recall that for two algebras Λ and Π, an equivalence modΛ → modΠ is called a stab...
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Two unital dual operator algebras A,B are called ∆-equivalent if there exists an equivalence functor F : AM → BM which “extends” to a ∗−functor implementing an equivalence between the categories ADM and BDM. Here AM denotes the category of normal representations of A and ADM denotes the category with the same objects as AM and ∆(A)-module maps as morphisms (∆(A) = A ∩A ). We prove that any such...
متن کاملRepresentation Type and Stable Equivalence of Morita Type for Finite Dimensional Algebras
In this note we show that two nite dimensional algebras have the same representation type if they are stably equivalent of Morita type. Stable equivalences of Morita type were introduced for blocks of group algebras by Brou e 2], see also 7]. The concept is motivated by a result of Rickard. In 9], he proved that any derived equivalence between nite dimensional self-injective algebras and ? indu...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2003
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-03-06831-x