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QUASI-HEREDITARY SKEW GROUP ALGEBRAS

Part of: Rings and algebras with additional structure Representation theory of rings and algebras

Published online by Cambridge University Press:  24 September 2024

ANNA RODRIGUEZ RASMUSSEN Open the ORCID record for ANNA RODRIGUEZ RASMUSSEN [Opens in a new window]
ANNA RODRIGUEZ RASMUSSEN*
Affiliation:
Department of Mathematics Uppsala University Lägerhyddsvägen 1 Uppsala Sweden
*
[email protected]
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Abstract

Given an algebra and a finite group acting on it via automorphisms, a natural object of study is the associated skew group algebra. In this article, we study the relationship between quasi-hereditary structures on the original algebra and on the corresponding skew group algebra. Assuming a natural compatibility condition on the partial order, we show that the skew group algebra is quasi-hereditary if and only if the original algebra is. Moreover, we show that in this setting an exact Borel subalgebra of the original algebra which is invariant as a set under the group action gives rise to an exact Borel subalgebra of the skew group algebra and that under this construction, properties such as normality and regularity of the exact Borel subalgebra are preserved.

Keywords

quasi-hereditary algebrasskew group algebrasexact Borel subalgebras

MSC classification

Primary: 16W22: Actions of groups and semigroups; invariant theory 16G20: Representations of quivers and partially ordered sets
Type
Article
Information
Nagoya Mathematical Journal , First View , pp. 1 - 44
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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