CQG algebras: a direct algebraic approach to compact quantum groups

Abstract

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.

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

References in corpus (1)

• General compact quantum groups, a tutorial

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