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The Dirac Operator on SU q (2)

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Abstract

We construct a 3+-summable spectral triple over the quantum group SU q (2) which is equivariant with respect to a left and a right action of The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order.

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Authors and Affiliations

  1. Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2-4, 34014, Trieste, Italy

    Ludwik Dabrowski & Walter van Suijlekom

  2. Dipartimento di Matematica e Informatica, Università di Trieste, Via Valerio 12/b, 34127, Trieste

    Giovanni Landi

  3. INFN, Sezione di Napoli, Napoli, Italy

    Giovanni Landi & Andrzej Sitarz

  4. Institute of Physics, Jagiellonian University, Reymonta 4, 30-059, Kraków, Poland

    Joseph C. Várilly

Authors
  1. Ludwik Dabrowski
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  2. Giovanni Landi
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  3. Andrzej Sitarz
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  4. Walter van Suijlekom
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  5. Joseph C. Várilly
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Additional information

Communicated by A. Connes

Partially supported by Polish State Committee for Scientific Research (KBN) under grant 2 P03B 022 25.

Regular Associate of the Abdus Salam ICTP, Trieste.

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Dabrowski, L., Landi, G., Sitarz, A. et al. The Dirac Operator on SU q (2). Commun. Math. Phys. 259, 729–759 (2005). https://doi.org/10.1007/s00220-005-1383-9

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  • DOI: https://doi.org/10.1007/s00220-005-1383-9

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