JournalsjncgVol. 8, No. 1pp. 45–59

On the Hochschild and cyclic (co)homology of rapid decay group algebras

  • Ronghui Ji

    Indiana University-Purdue University, Indianapolis, USA
  • Crichton Ogle

    Ohio State University, Columbus, USA
  • Bobby W. Ramsey

    University of Hawai‘i at Mānoa, USA
On the Hochschild and cyclic (co)homology of rapid decay group algebras cover
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Abstract

We show that the technical condition of solvable conjugacy bound, introduced in [JOR1], can be removed without affecting the main results of that paper. The result is a Burghelea-type description of the summands HHt(HB,L(G))x\mathrm{HH}_*^t({\mathcal{H}_{\mathcal{B},L}(G)})_{\langle x\rangle} and HCt(HB,L(G))x\mathrm{HC}_*^t({\mathcal{H}_{\mathcal{B},L}(G)})_{\langle x\rangle} for any bounding class B\mathcal{B}, discrete group with word-length (G,L)(G,L) and conjugacy class xG\langle x\rangle\in \langle G\rangle. We use this description to prove the conjecture B\mathcal{B}-SrBC of [JOR1] for a class of groups that goes well beyond the cases considered in that paper. In particular, we show that the conjecture 1\ell^1-SrBC (the Strong Bass Conjecture for the topological K-theory of 1(G)\ell^1(G)) is true for all semihyperbolic groups which satisfy SrBC, a statement consistent with the rationalized Bost conjecture for such groups.

Cite this article

Ronghui Ji, Crichton Ogle, Bobby W. Ramsey, On the Hochschild and cyclic (co)homology of rapid decay group algebras. J. Noncommut. Geom. 8 (2014), no. 1, pp. 45–59

DOI 10.4171/JNCG/148