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Symmetries of Kirchberg algebras | | David J. Benson
; Alex Kumjian
; N. Christopher Phillips
; | | Date: |
22 Feb 2003 | | Subject: | Operator Algebras MSC-class: 20C10, 46L55 (Primary) 19K99, 19L47, 46L40, 46L80 (Secondary) | math.OA | | Abstract: | Let A be a separable unital nuclear purely infinite simple C*-algebra satisfying the Universal Coefficient Theorem, and such that the K_0-class of the identity is zero. We prove that every automorphism of order two of the K-theory of A is implemented by an automorphism of A of order two. As a consequence, we prove that every countable Z/2Z-graded module over the representation ring of Z/2Z is isomorphic to the equivariant K-theory for some action of Z/2Z on a separable unital nuclear purely infinite simple C*-algebra. Along the way, we prove that every not necessarily finitely generated module over the group ring of Z/2Z which is free as an abelian group has a direct sum decomposition with only three kinds of summands, namely the group ring itself and Z on which the nontrivial element of Z/2Z acts either trivially or by multiplication by -1. | | Source: | arXiv, math.OA/0302273 | | Services: | Forum | Review | PDF | Favorites | |
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