finite quantum group


Definition 0.1.

A finite quantum group QGf is a pair (,Φ) of a finite-dimensional C*-algebraPlanetmathPlanetmath with a comultiplication Φ such that (,Φ) is a Hopf *-algebra.

Note that one obtains the dual Hopf algebraMathworldPlanetmathPlanetmathPlanetmath of a commutativePlanetmathPlanetmathPlanetmath, finite quantum group via Fourier transformationPlanetmathPlanetmath of the group’s elements.

References

  • 1 Abe, E., Hopf Algebras, Cambridge University Press, 1977.
  • 2 Sweedler, M. E., Hopf Algebras, W.A. Benjamin, inc., New York, 1969.
  • 3 Kustermans, J., Van Daele, A., C*-algebraic Quantum GroupsPlanetmathPlanetmath arising from Algebraic Quantum Groups, Int. J. of Math. 8 (1997), 1067-1139.
  • 4 Lance, E.C., An explicit description of the fundamental unitary for SU(2)q, Commun. Math. Phys. 164 (1994), 1-15.
Title finite quantum group
Canonical name FiniteQuantumGroup
Date of creation 2013-03-22 18:24:10
Last modified on 2013-03-22 18:24:10
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 17
Author bci1 (20947)
Entry type Definition
Classification msc 46L05
Classification msc 81R15
Classification msc 81R50
Synonym quantum group
Synonym dual of a finite Hopf algebra
Related topic CompactQuantumGroup
Related topic HopfAlgebra
Related topic GrassmanHopfAlgebrasAndTheirDualCoAlgebras
Related topic CompactMatrixQuantumGroup
Defines comultiplication in a quantum group
Defines dual of a finite Hopf algebra