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- W2012162267 abstract "Abstract Let G 0 and G 1 be countable abelian groups. Let γ i be an automorphism of G i of order two. Then there exists a unital Kirchberg algebra A satisfying the Universal Coefficient Theorem and with [1 A ] = 0 in K 0 (A), and an automorphism α ∈ Aut(A) of order two, such that K 0 (A) ≅ G 0 , such that K 1 (A) ≅ G 1 , and such that α * : K i (A) → K i (A) is γ i . As a consequence, we prove that every -graded countable module over the representation ring R( ) of is isomorphic to the equivariant K-theory K (A) for some action of on a unital Kirchberg algebra A . Along the way, we prove that every not necessarily finitely generated [ ]-module which is free as a -module has a direct sum decomposition with only three kinds of summands, namely [ ] itself and on which the nontrivial element of acts either trivially or by multiplication by −1." @default.
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- W2012162267 date "2003-12-01" @default.
- W2012162267 modified "2023-10-01" @default.
- W2012162267 title "Symmetries of Kirchberg Algebras" @default.
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- W2012162267 doi "https://doi.org/10.4153/cmb-2003-049-7" @default.
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