A LINEAR APPROACH TO LIE TRIPLE AUTOMORPHISMS OF H^*-ALGEBRAS
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By developing a linear algebra program involving many different structures associated to a three-graded H*-algebra, it is shown that if L is a Lie triple automorphism of an in nite-dimensional topologically simple associative H*-algebra A, then L is either an automorphism, an anti-automorphism, the negative of an automorphism or the negative of an anti-automorphism. If A is finite-dimensional, then there exists an automorphism, an anti-automorphism, the negative of an automorphism or the negative of an anti-automorphism F : A → A such that δ := F -L is a linear map from A onto its center sending commutators to zero. We also describe L in the case of having A zero annihilator.
Abstract
By developing a linear algebra program involving many different structures associated to a three-graded H*-algebra, it is shown that if L is a Lie triple automorphism of an in nite-dimensional topologically simple associative H*-algebra A, then L is either an automorphism, an anti-automorphism, the negative of an automorphism or the negative of an anti-automorphism. If A is finite-dimensional, then there exists an automorphism, an anti-automorphism, the negative of an automorphism or the negative of an anti-automorphism F : A → A such that δ := F -L is a linear map from A onto its center sending commutators to zero. We also describe L in the case of having A zero annihilator.
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