| 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.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 240, 1997, pp. 53–66. |
