Use this URL to cite or link to this record in EThOS: | http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.688100 |
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Title: | On separable equivalence of finite dimensional algebras | ||||
Author: | Peacock, Simon F. |
ISNI:
0000 0004 5916 7585
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Awarding Body: | University of Bristol | ||||
Current Institution: | University of Bristol | ||||
Date of Award: | 2015 | ||||
Availability of Full Text: |
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Abstract: | |||||
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.
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Supervisor: | Not available | Sponsor: | Not available | ||
Qualification Name: | Thesis (Ph.D.) | Qualification Level: | Doctoral | ||
EThOS ID: | uk.bl.ethos.688100 | DOI: | Not available | ||
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