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Compact Induced Representations

Published online by Cambridge University Press:  20 November 2018

Robert C. Busby  and
Irwin Schochetman
Robert C. Busby
Affiliation:
Drexel University, Philadelphia, Pennsylvania
Irwin Schochetman
Affiliation:
Oakland University, Rochester, Michigan
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In [15; 16; 17], Horst Leptin introduced what he called generalized group algebras. These Banach *-algebras are formed by letting a locally compact group G act on a Banach *-algebra A both by *-automorphisms and by a cocycle with values in the multiplier algebra, M (A ), of A. We will review the precise construction later, but for now we remark that examples include the group algebra of a group extension, the covariance algebras of quantum field theory, the “projective group algebras” of a group G (that is, for each complex-valued cocycle λ, called a multiplier in the literature, the Banach *-algebra whose nondegenerate *-representations are in bijective correspondence with the λ-projective representations of G), and the twisted group algebras of Edwards and Lewis [8; 9].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 1 , February 1972 , pp. 5 - 16
Copyright
Copyright © Canadian Mathematical Society 1972

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