Titlebook: Kac Algebras and Duality of Locally Compact Groups; Michel Enock,Jean-Marie Schwartz Book 1992 Springer-Verlag Berlin Heidelberg 1992 Abel

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Co-Involutive Hopf-Von Neumann Algebras,t and a co-involution, which are nothing but the duals of the usual product and involution of the involutive Banach algebra .. (.) of all (classes of) integrable (with respect to a left Haar measure) complex valued functions on . (let us recall that .. (.) is the predual of ..(.)).

FLACK

adduction

Introduction,set of characters of an abelian locally compact group . is an abelian group, called the dual group of ., and noted ., which is locally compact for a suitable topology. Moreover, the bidual .ˆˆ is canonically isomorphic and homeomorphic to . the Fourier transform carries the convolution algebra ..(.)

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Co-Involutive Hopf-Von Neumann Algebras, Kirchberg ([79]), and de Cannière and the authors ([21]). The paradigm, from which the whole theory comes, is the algebra ..(G) of all the (classes of) essentially bounded measurable (with respect to a left Haar measure) complex valued functions on a locally compact group .,equipped with a coproduc

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Kac Algebras,rman and Kac ([180]). On a co-involutive Hopf-von Neumann algebra (., ., .), a Haar weight is a faithful, semi-finite, normal weight on .., which is left-invariant with respect to ., i.e. such that: . for all . in .. (in 2.5, we show, after Kirchberg, that this axiom may be weakened), and, roughly s

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Representations of a Kac Algebra; Dual Kac Algebra,r and . the von Neumann algebra generated by λ. This chapter deals with the representations of the Banach algebra M., following Kirchberg ([79]) and de Cannière and the authors ([21]), and the construction of the dual Kac algebra, as found independently by the authors ([34]) and Vainermann and Kac (

Aromatic

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e used for illustrating the underlying ideas and concepts and links to other fields of physics are provided. After an introduction to undulator radiation and the low-gain FEL, the one-dimensional theory of the high-gain FEL is developed in a systematic way. Particular emphasis is put on explaining a