Separable equivalence, complexity and representation type

Simon F. Peacock

Research output: Contribution to journalArticle (Academic Journal)

6 Citations (Scopus)
223 Downloads (Pure)

Abstract

We generalise the notion of separable equivalence, originally presented by Linckelmann in [13], to an equivalence relation on additive categories. We use this generalisation to show that from an initial equivalence between two algebras we may build equivalences between many related categories. We also show that separable equivalence preserves the representation type of an algebra. This generalises Linckelmann's result in [13], where he showed this in the case of symmetric algebras. We use these theorems to show that the group algebras of several small cyclic groups cannot be separably equivalent. This gives several examples of algebras that have the same complexity but are not separably equivalent.
Original languageEnglish
Pages (from-to)219-240
Number of pages22
JournalJournal of Algebra
Volume490
Early online date25 Jul 2017
DOIs
Publication statusPublished - 15 Nov 2017

Keywords

  • Separable equivalence
  • Complexity
  • Representation type

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