A Complete Formulation of Baum-Conens' Conjecture for the Action of Discrete Quantum Groups

Simple item page
dc.creatorGoswami, Debashish
dc.creatorKuku, A. O.
dc.date2003-10-30
dc.date.accessioned2026-07-07T05:02:21Z
dc.date.available2026-07-07T05:02:21Z
dc.descriptionWe formulate a version of Baum-Connes' conjecture for a discrete quantum group, building on our earlier work (\cite{GK}). Given such a quantum group $\cla$, we construct a directed family $\{\cle_F \}$ of $C^*$-algebras ($F$ varying over some suitable index set), borrowing the ideas of \cite{cuntz}, such that there is a natural action of $\cla$ on each $\cle_F$ satisfying the assumptions of \cite{GK}, which makes it possible to define the "analytical assembly map", say $μ^{r,F}_i$, $i=0,1,$ as in \cite{GK}, from the $\cla$-equivariant $K$-homolgy groups of $\cle_F$ to the $K$-theory groups of the "reduced" dual $\hat{\cla_r}$ (c.f. \cite{GK} and the references therein for more details). As a result, we can define the Baum-Connes' maps $μ^r_i : \stackrel{\rm lim}{\longrightarrow} KK_i^\cla(\cle_F,\IC) \raro K_i(\hat{\cla_r}),$ and in the classical case, i.e. when $\cla$ is $C_0(G)$ for a discrete group, the isomorphism of the above maps for $i=0,1$ is equivalent to the Baum-Connes' conjecture. Furthermore, we verify its truth for an arbitrary finite dimensional quantum group and obtain partial results for the dual of $SU_q(2).$
dc.descriptionto appear in "K Theory" (special volume for H. Bass). A preliminary version was available as ICTP preprint since the early this year
dc.identifierhttps://arxiv.org/abs/math/0310470
dc.identifierhttp://arxiv.org/abs/math/0310470
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69025
dc.subjectK-Theory and Homology
dc.subjectOperator Algebras
dc.subject19K35, 46L80,81R50
dc.titleA Complete Formulation of Baum-Conens' Conjecture for the Action of Discrete Quantum Groups
dc.typetext

Files

Collections

arXiv