The Dirac operator on compact quantum groups
نویسندگان
چکیده
منابع مشابه
The Dirac Operator on Compact Quantum Groups
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...
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Given a (reduced) locally compact quantum group A, we can consider the convolution algebra L(A) (which can be identified as the predual of the von Neumann algebra form of A). It is conjectured that L(A) is operator biprojective if and only if A is compact. The “only if” part always holds, and the “if” part holds for Kac algebras. We show that if the splitting morphism associated with L(A) being...
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In this paper we show how to construct a Dirac operator on a lattice in complete analogy with the continuum. In fact we consider a more general problem, that is, the Dirac operator over an abelian finite group (for which a lattice is a particular example). Our results appear to be in direct connexion with the so called fermion doubling problem. In order to find this Dirac operator we need to in...
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A kind of Dirac-Connes operator defined in the framework of Connes’ NCG is introduced on discrete abelian groups; it satisfies a Junk-free condition, and bridges the NCG composed by Dimakis, MüllerHoissen and Sitarz and the NCG of Connes. Then we apply this operator to d-dimensional lattices. [email protected] [email protected]
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2010
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle.2010.026