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\(C\)-algebras and algebras in Plancherel duality. (English. Russian original) Zbl 0960.16046

J. Math. Sci., New York 96, No. 5, 3478-3485 (1999); translation from Zap. Nauchn. Semin. POMI 240, 53-66 (1997).
Summary: For an arbitrary (possibly noncommutative) \(C\)-algebra, a positivity condition generalizing the Krein condition for the 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.

MSC:

16W30 Hopf algebras (associative rings and algebras) (MSC2000)
05E30 Association schemes, strongly regular graphs
16D90 Module categories in associative algebras
15A30 Algebraic systems of matrices

Citations:

Zbl 0930.00010
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References:

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