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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Actions of compact quantum groups
on $C^*$-algebras


Author: Marcin Marciniak
Journal: Proc. Amer. Math. Soc. 126 (1998), 607-616
MSC (1991): Primary 22D25; Secondary 46L60, 81R50
MathSciNet review: 1415332
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Abstract: In this paper we investigate a structure of the fixed point algebra under an action of compact matrix quantum group on a $C^*$-algebra $\mathcal{B}$. We also show that the categories of $\mathcal C$-comodules in $\mathcal B$ and inner endomorphisms restricted to the fixed point algebra coincide when the relative commutant of the fixed point algebra is trivial. Next we show a version of the Tannaka duality theorem for twisted unitary groups.


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Additional Information

Marcin Marciniak
Affiliation: Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland
Email: matmm@univ.gda.pl

DOI: https://doi.org/10.1090/S0002-9939-98-04066-0
Received by editor(s): May 7, 1996
Received by editor(s) in revised form: July 16, 1996, and August 8, 1996
Additional Notes: The author was supported by KBN grant 2 P301 020 07
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society