1 Finite Quantum (Hopf) Algebra
Recall that:
Definition 1.1. A finite quantum group QGf is a pair (ℍ, Φ) of a finite-dimensional
C∗-algebra ℍ with a comultiplication Φ such that (ℍ, Φ) is a Hopf ∗-algebra.
Definition 1.2. A finite quantum algebra AGf is the dual of a finite quantum group
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.
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 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.
