finite quantum group

Definition 0.1.

A finite quantum group $Q_{Gf}$ is a pair $(\\mathbb{H},\\Phi)$ of a finite-dimensional $C^{*}$ -algebra $\\mathbb{H}$ with a comultiplication $\\Phi$ such that $(\\mathbb{H},\\Phi)$ is a Hopf ${}^{*}$ -algebra.

Note that one obtains the dual Hopf algebra of a commutative, finite quantum group viaFourier transformation 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 Groups arising fromAlgebraic 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.

单词	FiniteQuantumGroup
释义	finite quantum group Definition 0.1. A finite quantum group $Q_{Gf}$ is a pair $(\\mathbb{H},\\Phi)$ of a finite-dimensional $C^{}$ -algebra $\\mathbb{H}$ with a comultiplication $\\Phi$ such that $(\\mathbb{H},\\Phi)$ is a Hopf ${}^{}$ -algebra. Note that one obtains the dual Hopf algebra of a commutative, finite quantum group viaFourier transformation 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 Groups arising fromAlgebraic 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.
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