Geodesic
$C$-algebras and algebras in Plancherel duality
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Tome 240 (1997), pp. 53-66 Cet article a éte moissonné depuis la source Math-Net.Ru

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For an arbitrary $C$-algebra (possibly non-commutative) 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 non-commutative). 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 being commutative. 
@article{ZNSL_1997_240_a3,
     author = {A. M. Vershik and S. A. Evdokimov and I. N. Ponomarenko},
     title = {$C$-algebras and algebras in {Plancherel} duality},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {53--66},
     year = {1997},
     volume = {240},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a3/}
}
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A. M. Vershik; S. A. Evdokimov; I. N. Ponomarenko. $C$-algebras and algebras in Plancherel duality. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Tome 240 (1997), pp. 53-66. http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a3/