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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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