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
Sage, D. (2002). Group actions on central simple algebras. Journal of Algebra, 250 (1), 18-43. https://doi.org/10.1006/jabr.2001.9098