Unitary invariance in algebraic algebras

Lanski, Charles

doi:10.1090/S0002-9947-1978-0511403-1

Unitary invariance in algebraic algebras
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by Charles Lanski PDF

Trans. Amer. Math. Soc. 245 (1978), 139-146 Request permission

Abstract:

A structure theorem is obtained for subspaces invariant under conjugation by the unitary group of a prime algebraic algebra over an infinite field. For an invariant subalgebra W, it is shown that either W is central, W contains an ideal, or the ring satisfies the standard identity of degree eight. Also, for prime algebras not satisfying such an identity, the unitary group is not solvable.

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Open questions on rings with involution