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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)
  • Received : 2009.04.22
  • Published : 2011.01.01

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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