Chern character for the Schwartz algebra of p-adic GL(n)
K-Theory and Homology
2007-05-23 v1 Operator Algebras
Abstract
We construct a Chern character map from the K-theory of the reduced C^* algebra of the p-adic GL(n) with values in the periodic cyclic homology of the Schwartz algebra of this group. We prove that this map is an isomorphism after tensoring with C by comparing an explicit formula, stated in the algebraic case by Cuntz and Quillen, with the classical Chern character. This Chern character is a crucial ingredient in the proof of the Baum-Connes conjecture for the p-adic GL(n) due to Baum, Higson and Plymen.
Keywords
Cite
@article{arxiv.math/0002131,
title = {Chern character for the Schwartz algebra of p-adic GL(n)},
author = {Jacek Brodzki and Roger Plymen},
journal= {arXiv preprint arXiv:math/0002131},
year = {2007}
}