Derived equivalences of algebras

Xi, Changchang

doi:10.1112/blms.12209

Cited by 3 publications

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“…To get derived equivalences, the following corollary of [15, Theorem1.1] provides a convenient way. For further information on constructions of derived equivalences of algebras, we refer to [33].…”

Section: Derived Equivalences Of Algebrasmentioning

confidence: 99%

Derived equivalences between triangular matrix algebras

2017

Communications in Algebra

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The centralizer of a matrix in a full matrix algebra is called a principal centralizer matrix algebra. Characterizations are presented for principal centralizer matrix algebras to be Morita equivalent, almost ν-stable derived equivalent, derived equivalent, and stably equivalent of Morita type, respectively, in terms of new equivalence relations on square matrices. These equivalence relations on matrices are introduced in a natural way by their elementary divisors. Thus the categorical equivalences are reduced to questions in linear algebra. Consequently, principal centralizer matrix algebras of permutation matrices are Morita equivalent if and only if they are derived equivalent. Moreover, two representation-finite, principal centralizer matrix algebras over a perfect field are stably equivalent of Morita type if and only if they are stably equivalent. Further, derived equivalences between the principal centralizer matrix algebras of permutation matrices induce the ones of their p-regular parts and p-singular parts of the given permutations.

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Section: Derived Equivalences Of Algebrasmentioning

confidence: 99%