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finite quantum group
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(Definition)
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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 via Fourier transformation of the group's elements.
- 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 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.
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"finite quantum group" is owned by bci1.
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Cross-references: group's, transformation, commutative, Hopf algebra, comultiplication, finite-dimensional
There are 2 references to this entry.
This is version 14 of finite quantum group, born on 2008-09-20, modified 2009-06-05.
Object id is 11049, canonical name is FiniteQuantumGroup.
Accessed 1335 times total.
Classification:
| AMS MSC: | 81R50 (Quantum theory :: Groups and algebras in quantum theory :: Quantum groups and related algebraic methods) | | | 81R15 (Quantum theory :: Groups and algebras in quantum theory :: Operator algebra methods) | | | 46L05 (Functional analysis :: Selfadjoint operator algebras :: General theory of $C^*$-algebras) |
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Pending Errata and Addenda
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