Derived equivalences and stable equivalences of Morita type, I
نویسندگان
چکیده
منابع مشابه
A Note on Stable Equivalences of Morita Type
We investigate when an exact functor F ∼= − ⊗Λ MΓ : mod-Λ → mod-Γ which induces a stable equivalence is part of a stable equivalence of Morita type. If Λ and Γ are finite dimensional algebras over a field k whose semisimple quotients are separable, we give a necessary and sufficient condition for this to be the case. This generalizes a result of Rickard’s for self-injective algebras. As a corol...
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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...
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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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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 2010
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000010199