Compact quantum group C^*-algebras as Hopf algebras with approximate unit

Details Compact quantum group C^*-algebras as Hopf algebras with approximate unit Compact quantum group C^*-algebras as Hopf algebras with approximate unit

1999-04-30

arxiv.org/abs/math/9904175v1

Mathematics

Quantum Algebra

15 pages, latex 2e, amsart style

Scientific paper

In this paper we construct and study the representation theory of a Hopf C^*-algebra with approximate unit, which constitutes quantum analogue of a compact group C^*-algebra. The construction is done by first introducing a convolution-product on an arbitrary Hopf algebra H with integral, and then constructing the L_2 and C^*-envelopes of H (with the new convolution-product) when H is a compact Hopf *-algebra.

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