Sergey Neshveyev

THE DIRAC OPERATOR ON COMPACT QUANTUM GROUPS

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.

Ergodicity of the action of the positive rationals on the group of finite adeles and the Bost-Connes phase transition theorem

We study relatively invariant measures with the multiplicators Q* + q? q -β on the space A f of finite adeles. We prove that for β∈ (0, 1] such measures are ergodic, and then deduce from this the uniqueness of KMS β -states for the Bost-Connes system. Combining this with a result of Blackadar and Boca-Zaharescu, we also obtain ergodicity of the action of Q* on the full adeles.

Drinfeld Center and Representation Theory for Monoidal Categories

Motivated by the relation between the Drinfeld double and central property (T) for quantum groups, given a rigid C*-tensor category

The variational principle for a class of asymptotically abelian C ∗ -algebras

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ON SECOND COHOMOLOGY OF DUALS OF COMPACT GROUPS

C and a unitary half-braiding on an ind-object, we construct a *-representation of the fusion algebra of

ENTROPY OF BOGOLIUBOV AUTOMORPHISMS OF CAR AND CCR ALGEBRAS WITH RESPECT TO QUASI-FREE STATES

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