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The Dirac operator on compact quantum groups
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Sergey Neshveyev
Published/Copyright:
January 20, 2010
Abstract
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 U𝔤 ⊗ 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 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.
Received: 2007-06-21
Published Online: 2010-01-20
Published in Print: 2010-April
© Walter de Gruyter Berlin · New York 2010
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Articles in the same Issue
- The Dirac operator on compact quantum groups
- Pair correlation of sums of rationals with bounded height
- Existence and uniqueness of constant mean curvature foliation of asymptotically hyperbolic 3-manifolds II
- Crossed products by minimal homeomorphisms
- On the facial structure of the unit ball in a JB*-triple
- Adjoint ideals along closed subvarieties of higher codimension
- On surfaces of general type with maximal Albanese dimension
- A basic set for the alternating group
- The twisted fourth moment of the Riemann zeta function
