The Dirac operator on compact quantum groups
Journal article, Peer reviewed
Åpne
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https://hdl.handle.net/10642/1003Utgivelsesdato
2010-01-20Metadata
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Originalversjon
Neshveyev, S., Tuset, L. (2010). The Dirac operator on compact quantum groups. Journal für die reine und angewandte Mathematik, 2010 (641), 1-20. http://dx.doi.org/10.1515/CRELLE.2010.026Sammendrag
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 UgnClðgÞ. 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 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.