2003/02/22 by David J. Benson, Benson, David J., Alex Kumjian +3 · 1 citation
Mathematics · Physics and Astronomy · #19L47 #20C10 #46L40 #46L55 (Primary) 19K99 #46L80 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.OA #msc:19K99 #msc:19L47 #msc:20C10 #msc:46L40 #msc:46L55 #msc:46L80
paper · pdf · doi:10.48550/arxiv.math/0302273
18 pages, AMSLaTeX
arxiv created 2003/02/22 · openalex publication_date 2003/02/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be a separable unital nuclear purely infinite simple C*-algebra satisfying the Universal Coefficient Theorem, and such that the K0-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.