Duality for the quantum E(2) group

Alfons Van Daele and S. L. Woronowicz

Vol. 173 (1996), No. 2, 375–385

DOI: 10.2140/pjm.1996.173.375

Abstract

The quantum deformation E_μ(2) of the group of motions of the plane on the C^∗-level was obtained by the second author. He also constructed the Pontryagin dual Ê_μ(2) explicitly, together with the unitary bicharacter describing this duality. In this paper we show that the dual of Ê_μ(2) is again E_μ(2).

Mathematical Subject Classification 2000

Primary: 46L87

Secondary: 16W30, 17B37, 22D25, 46L60, 81R50

Milestones

Received: 6 October 1993

Revised: 1 June 1994

Published: 1 April 1996