Equivariant spectral triples and Poincare duality for SUq(2)

Chakraborty, Partha Sarathi ; Pal, Arupkumar (2010) Equivariant spectral triples and Poincare duality for SUq(2) Transactions of the American Mathematical Society . pp. 1-17. ISSN 0002-9947

PDF - Author Version

Official URL: http://citeseerx.ist.psu.edu/viewdoc/download?doi=...


Let A be the C-algebra associated with SUq(2), let π be the representation by left multiplication on the L2 space of the Haar state and let D be the equivariant Dirac operator for this representation constructed by the authors earlier. We prove in this article that there is no operator other than the scalars in the commutant π(A)' that has bounded commutator with D. This implies that the equivariant spectral triple under consideration does not admit a rational Poincare dual in the sense of Moscovici, which in particular means that this spectral triple does not extend to a K-homology fundamental class for SUq(2). We also show that a minor modification of this equivariant spectral triple gives a fundamental class and thus implements Poincare duality.

Item Type:Article
Source:Copyright of this article belongs to American Mathematical Society.
ID Code:89581
Deposited On:28 Apr 2012 12:51
Last Modified:19 May 2016 04:05

Repository Staff Only: item control page