Download Kac Algebras and Duality of Locally Compact Groups by Michel Enock,Jean-Marie Schwartz,A. Connes PDF

By Michel Enock,Jean-Marie Schwartz,A. Connes

This publication offers with the speculation of Kac algebras and their twin­ ity, elaborated independently by means of M. Enock and J . -M. Schwartz, and via G. !. Kac and L. !. Vajnermann within the seventies. The sub­ ject has now reached a nation of adulthood which totally justifies the ebook of this booklet. additionally, in recent years, the subject of "quantum teams" has turn into extremely popular and attracted the eye of a growing number of mathematicians and theoret­ ical physicists. One remains to be lacking an outstanding characterization of quantum teams between Hopf algebras, just like the nature­ ization of Lie teams between in the neighborhood compact teams. it truly is therefore super worthy to enhance the final thought, as this e-book does, with emphasis at the analytical facets of the topic rather than the in basic terms algebraic ones. the unique motivation of M. Enock and J. -M. Schwartz will be formulated as follows: whereas within the Pontrjagin duality conception of in the community compact abelian teams an ideal symmetry exists among a gaggle and its twin, this is often not actual within the quite a few duality theorems of T. Tannaka, M. G. Krein, W. F. Stinespring . . . facing non abelian in the community compact teams. the purpose is then, within the line proposed by way of G. !. Kac in 1961 and M. Takesaki in 1972, to discover an exceptional class of Hopf algebras, containing the class of in the community compact teams and pleasing an ideal duality.

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