Acta Applicandae Mathematica

, Volume 31, Issue 1, pp 75–85 | Cite as

Haar measures on HopfC*-algebras

  • Xiu-Chi Quan


In this paper, we first use Markov-Kakutani's fixed point theorem to prove the existence and uniqueness of Haar measures on cocommutative HopfC*-algebras. Also we show that in the commutative case, there exists a natural one-to-one correspondence between the Haar measure on a given HopfC*-algebra and Haar measures on the associated semigroup. Finally, we show that for HopfC*-algebras with Peter-Weyl property, they have Haar measures.

Mathematics Subject Classifications (1991)

22D25 22D35 43A40 46L89 

Key words

Haar measure HopfC*-algebra fixed points quantum group 


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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Xiu-Chi Quan
    • 1
  1. 1.Institute of Fundamental TheoryUniversity of FloridaGainesvilleUSA

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