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http://dx.doi.org/10.4134/JKMS.2011.48.1.117

A LINEAR APPROACH TO LIE TRIPLE AUTOMORPHISMS OF H*-ALGEBRAS  

Martin, A. J. Calderon (DEPARTAMENTO DE MATEMATICAS UNIVERSIDAD DE CADIZ)
Gonzalez, C. Martin (DEPARTAMENTO DE ALGEBRA GEOMETRIA Y TOPOLOGIA UNIVERSITY DE MALAGA)
Publication Information
Journal of the Korean Mathematical Society / v.48, no.1, 2011 , pp. 117-132 More about this Journal
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 infinite-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 $\rightarrow$ A such that $\delta$:= 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.
Keywords
H*-algebra; graded algebra; Jordan pair; Lie triple automorphism;
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