An Operator Algebraic Framework for the Duality of Quantum Groups

Tetsuya Masuda and Yoshiomi Nakagami
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Tetsuya Masuda: University of Tsukuba, Institute of Mathematics
Yoshiomi Nakagami: Yokohama City University, Department of Mathematics

A chapter in Mathematical Physics X, 1992, pp 291-295 from Springer

Abstract: Abstract The duality for a locally compact group established by Pontrjagin, Tannaka, Krein, Steinspring, Eymard and Tatsuuma is an important theoretical basis for the harmonic analysis. At the formal level of pure algebras, the notion of Hopf algebras is used to deal with the algebraic groups, discrete groups, or their dual objects at the same time. In order to control the infinite dimensional unitary representations, functional analysis is necessarily combined with the algebraic framework of Hopf algebras. This consideration suggests us to introduce the notion of Kac-algebras in the language of the Neumann algebras, in with the above mentioned duality is generalized by Kac [5], Takesaki [9] and Enock and Schwartz [2].

Date: 1992
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DOI: 10.1007/978-3-642-77303-7_24

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