CQG algebras: a direct algebraic approach to compact quantum groups

Details CQG algebras: a direct algebraic approach to compact quantum groups CQG algebras: a direct algebraic approach to compact quantum groups

1994-06-08

arxiv.org/abs/hep-th/9406042v1

Lett.Math.Phys. 32 (1994) 315-330

Physics

High Energy Physics

High Energy Physics - Theory

14 pp., Plain TeX, accepted by Lett. Math. Phys

Scientific paper

10.1007/BF00761142

The purely algebraic notion of CQG algebra (algebra of functions on a compact quantum group) is defined. In a straightforward algebraic manner, the Peter-Weyl theorem for CQG algebras and the existence of a unique positive definite Haar functional on any CQG algebra are established. It is shown that a CQG algebra can be naturally completed to a $C^\ast$-algebra. The relations between our approach and several other approaches to compact quantum groups are discussed.

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