Fourier Transform for Paragroups and Its Application to the Depth Two Case | Zendy

Nobuya Sato | Zendy

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Fourier Transform for Paragroups and Its Application to the Depth Two Case

Author(s) -

Nobuya Sato

Publication year - 1997

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195145447

Subject(s) - mathematics , flatness (cosmology) , multiplicative function , fourier transform , crossed product , algebra over a field , construct (python library) , discrete fourier transform (general) , string theory , pure mathematics , action (physics) , dual (grammatical number) , product (mathematics) , fourier analysis , fractional fourier transform , mathematical analysis , mathematical physics , geometry , computer science , quantum mechanics , art , physics , literature , cosmology , programming language

We prove that the flatness condition in Ocneanu's paragroup theory for graphs with depth two is equivalent to existence of the multiplicative unitaries in the theory of Baaj-Skandalis by using "Fourier transform" introduced by A. Ocneanu. Moreover, from two Kac algebras dual to each other, we construct a subfactor as a crossed product by a Kac algebra action, with the string algebra construction.

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