Unitary invariance in algebraic algebras

Author:
Charles Lanski

Journal:
Trans. Amer. Math. Soc. **245** (1978), 139-146

MSC:
Primary 16A28; Secondary 16A45

DOI:
https://doi.org/10.1090/S0002-9947-1978-0511403-1

MathSciNet review:
511403

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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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1978-0511403-1

Keywords:
Unitary group,
skew-symmetric elements,
Lie commutation,
invariant subspace,
invariant subring,
solvable normal subgroup

Article copyright:
© Copyright 1978
American Mathematical Society