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

Yuji Konishi, Masaru Nagisa and Yasuo Watatani

Vol. 153 (1992), No. 1, 119–127

DOI: 10.2140/pjm.1992.153.119

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.

Mathematical Subject Classification 2000

Primary: 46L55

Secondary: 16W30, 58B30

Milestones

Received: 4 April 1990

Published: 1 March 1992