Title

Group actions on central simple algebras

Document Type

Article

Publication Date

4-1-2002

Abstract

Let G be a group, F a field, and A a finite-dimensional central simple algebra over F on which G acts by F-algebra automorphisms. We study the subalgebras and ideals of A which are preserved by the group action. We prove a structure theorem and two classification theorems for invariant subalgebras under suitable hypotheses on A. We illustrate these results in the case of compact connected Lie groups and give some other applications. We also classify invariant ideals. © 2002 Elsevier Science (USA).

Publication Source (Journal or Book title)

Journal of Algebra

First Page

18

Last Page

43

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