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AN INTRODUCTION TO NONCOMMUTATIVE DIFFERENTIAL GEOMETRY ON QUANTUM GROUPS

  • ASCHIERI, PAOLO Dipartimento di Fisica Teorica, Via P. Giuria 1, 10125 Torino, Italy
  • CASTELLANI, LEONARDO Dipartimento di Fisica Teorica, Via P. Giuria 1, 10125 Torino, Italy
  • 2012-4-6
Published in:
  • International Journal of Modern Physics A. - World Scientific Pub Co Pte Lt. - 1993, vol. 08, no. 10, p. 1667-1706
Nuclear and High Energy Physics
Astronomy and Astrophysics
Atomic and Molecular Physics, and Optics
English We give a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case (q→1 limit). The Lie derivative and the contraction operator on forms and tensor fields are found. A new, explicit form of the Cartan-Maurer equations is presented. The example of a bicovariant differential calculus on the quantum group GL q(2) is given in detail. The softening of a quantum group is considered, and we introduce q curvatures satisfying q Bianchi identities, a basic ingredient for the construction of q gravity and q gauge theories.
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  • English
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green
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https://sonar.ch/global/documents/85440
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