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Zapiski Nauchnykh Seminarov POMI, 1997, Volume 240, Pages 53–66 (Mi znsl465)  
This article is cited in 3 scientific papers (total in 4 papers)

$C$-algebras and algebras in Plancherel duality

A. M. Vershika, S. A. Evdokimovb, I. N. Ponomarenkoa

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b St. Petersburg Institute for Informatics and Automation of RAS
Full-text PDF (211 kB) Citations (4)
Abstract: 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.
Received: 10.09.1996
English version:
Journal of Mathematical Sciences (New York), 1999, Volume 96, Issue 5, Pages 3478–3485
DOI: https://doi.org/10.1007/BF02175825
Bibliographic databases:
UDC: 517.896
Language: Russian
Citation: A. M. Vershik, S. A. Evdokimov, I. N. Ponomarenko, “$C$-algebras and algebras in Plancherel duality”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Zap. Nauchn. Sem. POMI, 240, POMI, St. Petersburg, 1997, 53–66; J. Math. Sci. (New York), 96:5 (1999), 3478–3485
Citation in format AMSBIB
\Bibitem{VerEvdPon97}
\by A.~M.~Vershik, S.~A.~Evdokimov, I.~N.~Ponomarenko
\paper $C$-algebras and algebras in Plancherel duality
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~II
\serial Zap. Nauchn. Sem. POMI
\yr 1997
\vol 240
\pages 53--66
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl465}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1691637}
\zmath{https://zbmath.org/?q=an:0960.16046}
\transl
\jour J. Math. Sci. (New York)
\yr 1999
\vol 96
\issue 5
\pages 3478--3485
\crossref{https://doi.org/10.1007/BF02175825}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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