Hopf C^∗-algebras and locally compact groups

Valéria Botelho de Magalhães Iório

Vol. 87 (1980), No. 1, 75–96

DOI: 10.2140/pjm.1980.87.75

Abstract

We define Hopf-C^∗-algebras and show one can associate to each locally compact group G a cocommutative Hopf-C^∗-algebras {C^∗(G),d} (here C^∗(G) is the C^∗-algebra of G) with involution and coidentity whose intrinsic group is isomorphic and homeomorphic to G. We also show that if the associated Hopf-C^∗-algebras are isomorphic then the groups are isomorphic and homeomorphic.

Mathematical Subject Classification 2000

Primary: 22D25

Secondary: 46L05, 16A24

Milestones

Received: 3 October 1978

Published: 1 March 1980