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Group Actions on Central Simple Algebras

✍ Scribed by Daniel S. Sage

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
197 KB
Volume
250
Category
Article
ISSN
0021-8693

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✦ Synopsis

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)

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