Some remarks on actions of compact matrix quantum groups on C*-algebras

Yuji Konishi; Masaru Nagisa; Yasuo Watatani

doi:10.2140/pjm.1992.153.119

Some remarks on actions of compact matrix quantum groups on C*-algebras

Yuji Konishi, Masaru Nagisa, Yasuo Watatani

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

In this paper we construct an action of a compact matrix quantum group on a Cuntz algebra or a UHF-algebra, and investigate the fixed point subalgebra of the algebra under the action. Especially we consider the action of _µU(2) on the Cuntz algebra O₂ and the action of S_µU(2) on the UHF-algebra of type 2^∞. We show that these fixed point subalgebras are generated by a sequence of Jones’ projections.

Original language	English
Pages (from-to)	119-127
Number of pages	9
Journal	Pacific Journal of Mathematics
Volume	153
Issue number	1
DOIs	https://doi.org/10.2140/pjm.1992.153.119
Publication status	Published - Mar 1992

All Science Journal Classification (ASJC) codes

Mathematics(all)

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AB - In this paper we construct an action of a compact matrix quantum group on a Cuntz algebra or a UHF-algebra, and investigate the fixed point subalgebra of the algebra under the action. Especially we consider the action of µU(2) on the Cuntz algebra O2 and the action of SµU(2) on the UHF-algebra of type 2∞. We show that these fixed point subalgebras are generated by a sequence of Jones’ projections.

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Some remarks on actions of compact matrix quantum groups on C*-algebras

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