Kac Algebras

Michel Enock and Jean-Marie Schwartz
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Michel Enock: Université Pierre et Marie Curie, CNRS, Laboratoire de Mathématiques Fondamentales
Jean-Marie Schwartz: Université Pierre et Marie Curie, CNRS, Laboratoire de Mathématiques Fondamentales

Chapter Chapter 2 in Kac Algebras and Duality of Locally Compact Groups, 1992, pp 44-82 from Springer

Abstract: Abstract This chapter deals with technical results about Haar weights, as they have been studied by the authors in [36] and [136], and, independently, by Vaĭnerman and Kac ([180]). On a co-involutive Hopf-von Neumann algebra (M, Γ, k), a Haar weight is a faithful, semi-finite, normal weight on M +, which is left-invariant with respect to Γ, i.e. such that: $$(i \otimes \varphi )\Gamma (x) = \varphi (x)1$$ for all x in M + (in 2.5, we show, after Kirchberg, that this axiom may be weakened), and, roughly speaking, satisfies two other axioms involving k. The quadruple (M, Γ, k, φ) is then called a Kac algebra.

Keywords: Compact Group; Left Ideal; Fourier Representation; Hilbert Algebra; Left Regular Representation (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1007/978-3-662-02813-1_3

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