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finite quantum algebra (Definition)

Finite Quantum (Hopf) Algebra

Recall that:

Definition 1.1   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.
Definition 1.2   A finite quantum algebra $A_{Gf}$ is the dual of a finite quantum group

$\displaystyle Q_{Gf}=(\mathbb{H},\Phi)$
as defined above. In the case of a commutative group, its dual commutative Hopf algebra is obtained by Fourier transformation of its dual finite Abelian quantum group elements.

Bibliography

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.



"finite quantum algebra" is owned by bci1.
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Keywords:  finite quantum groups

Cross-references: Hopf algebra, commutative group, finite quantum group

This is version 4 of finite quantum algebra, born on 2009-01-10, modified 2009-01-11.
Object id is 372, canonical name is FiniteQuantumGroup2.
Accessed 380 times total.

Classification:
Physics Classification: 03. (Quantum mechanics, field theories, and special relativity )
 03.65.Fd (Algebraic methods )
Pending Errata and Addenda
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