Abstract
For an arbitrary (possibly noncommutative) C-algebra, a positivity condition generalizing the Krein condition for a commutative case is defined. We show that the class of positive C-algebras includes those arising in algebraic combinatorics from association schemes (possibly noncommutative). It is proved that the category of positive C-algebras is equivalent to the category of pairs of algebras in Plancherel duality, one of which is commutative.
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 240, 1997, pp. 53–66.
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Vershik, A.M., Evdokimov, S.A. & Ponomarenko, I.N. C-algebras and algebras in plancherel duality. J Math Sci 96, 3478–3485 (1999). https://doi.org/10.1007/BF02175825
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DOI: https://doi.org/10.1007/BF02175825