Separable equivalence of algebras was introduced by Markus Linckelmann in [Linllb] and may be considered as an extension to the more well-known concepts of Morita, stable and derived equivalence. We will generalise the idea of separable equivalence of algebras to additive categories and demonstrate how a separable equivalence between algebras provides separable equivalences between several related categories. We will prove that there are several properties of an algebra that are invariant under separable equivalence. Specifically we show that if two algebras are separably equivalent then they must have the same complexity. We also show that the representation type of an algebra is preserved, including the finer grain classes of domestic and polynomial growth. Finally, if G is a finite group with elementary abelian Sylow p-subgroup P, then we use the separable equivalence of kG and kP to provide an upper bound for the representation dimension of kG, where k is an algebraically closed field of characteristic p.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:688100 |
| Date | January 2015 |
| Creators | Peacock, Simon F. |
| Publisher | University of Bristol |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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