The Dirac operator on compact quantum groups

Sergey Neshveyev, Lars Tuset
2010 Journal für die Reine und Angewandte Mathematik  
For the q-deformation Gq, 0 < q < 1, of any simply connected simple compact Lie group G we construct an equivariant spectral triple which is an isospectral deformation of that defined by the Dirac operator D on G. Our quantum Dirac operator Dq is a unitary twist of D considered as an element of U g ⊗ Cl(g). The commutator of Dq with a regular function on Gq consists of two parts. One is a twist of a classical commutator and so is automatically bounded. The second is expressed in terms of the
more » ... in terms of the commutator of the associator with an extension of D. We show that in the case of the Drinfeld associator the latter commutator is also bounded.
doi:10.1515/crelle.2010.026 fatcat:qvikzfwohndnhnenpd5ztmyycu