Lars Tuset - Quantum groups as non-commutative manifolds

For the q-deformation G_q, 0<q<1, of any simply connected simple compact Lie group G we construct a bi-equivariant spectral triple which is an isospectral deformation of that defined by the Dirac operator D of G. Our quantum Dirac operator D_q is a unitary twist of D considered as an element of the tensor product of U(g) with Cl(g). The twist is picked such that its boundary is the Drinfeld associator and using the KZ-equation we show that the commutator of D_q with a regular function on G_q is indeed bounded. Our Dirac operator provides equivariant spectral triples on all quantum homogenous spaces as well.

Joint work with Sergey Neshveyev.

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Last updated 30 April 2008. This page was created and is maintained by Stephen Wills (s.wills@ucc.ie).