The ring structure for equivariant twisted K-theory

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dc.creatorTu, Jean-Louis
dc.creatorXu, Ping
dc.date2006-04-07
dc.date2009-03-23
dc.date.accessioned2026-07-07T12:54:54Z
dc.date.available2026-07-07T12:54:54Z
dc.descriptionWe prove, under some mild conditions, that the equivariant twisted K-theory group of a crossed module admits a ring structure if the twisting 2-cocycle is 2-multiplicative. We also give an explicit construction of the transgression map $T_1: H^*(Γ;A) \to H^{*-1}((N\rtimes Γ;A)$ for any crossed module $N\to Γ$ and prove that any element in the image is $\infty$-multiplicative. As a consequence, we prove that, under some mild conditions, for a crossed module $N \to \gm$ and any $e \in \check{Z}^3(Γ;S^1)$, that the equivariant twisted K-theory group $K^*_{e,Γ}(N)$ admits a ring structure. As an application, we prove that for a compact, connected and simply connected Lie group G, the equivariant twisted K-theory group $K_{[c], G}^* (G)$ is endowed with a canonical ring structure $K^{i+d}_{[c],G}(G)\otimes K^{j+d}_{[c],G}(G)\to K^{i+j+d}_{[c], G}(G)$, where $d=dim G$ and $[c]\in H^2(G\rtimes G;S^1)$.
dc.description47 pages. To appear in Crelle
dc.identifierhttps://arxiv.org/abs/math/0604160
dc.identifierhttp://arxiv.org/abs/math/0604160
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224098
dc.subjectK-Theory and Homology
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectAlgebraic Topology
dc.subjectDifferential Geometry
dc.subjectOperator Algebras
dc.subject19L47 (Primary); 55N91, 46L80, 20L05 (Secondary)
dc.titleThe ring structure for equivariant twisted K-theory
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