Lie Group Actions on Simple Algebras
نویسنده
چکیده
Let G be a connected Lie group acting by algebra automorphisms on a finite-dimensional complex central simple algebra A. The algebra A is isomorphic to the endomorphism algebra of a projective representation V of G. We study the invariant subalgebras of A. In particular, we show that if V is irreducible, then the invariant subalgebras appear in dual pairs arising from factorizations of V . We apply this result to find a very simple description of the invariant subalgebras when G is compact. For example, if G is simple, the only stable subalgebras are A, C, and {0}. We also determine the invariant
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