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Algebra i Analiz, 1996, Volume 8, Issue 4, Pages 63–74 (Mi aa729)  
This article is cited in 34 scientific papers (total in 34 papers)

Research Papers

The Heisenberg double and the pentagon relation

R. M. Kashaevab

a St. Petersburg Branch of Steklov Mathematical Institute, St. Petersburg
b Laboratoire de Physique Théorique et à l'Université de Savoie, Lyon, France
Full-text PDF (392 kB) Citations (34)
Abstract: It is shown that the Heisenberg double of an arbitrary Hopf algebra has a canonical element satisfying the pentagon relation. The structure of the underlying algebras can be recovered by a given invertible constant solution of the pentagon relation. The Drinfeld double is representable as a subalgebra in the tensor square of the Heisenberg double. This offers a possibility of expressing solutions of the Yang–Baxter relation in terms of solutions of the pentagon relation.
Keywords: Heisenberg double, Drinfeld double, Yang–Baxter equation, pentagon relation.
Received: 25.12.1995
Bibliographic databases:
Document Type: Article
Language: English
Citation: R. M. Kashaev, “The Heisenberg double and the pentagon relation”, Algebra i Analiz, 8:4 (1996), 63–74; St. Petersburg Math. J., 8:4 (1997), 585–592
Citation in format AMSBIB
\Bibitem{Kas96}
\by R.~M.~Kashaev
\paper The Heisenberg double and the pentagon relation
\jour Algebra i Analiz
\yr 1996
\vol 8
\issue 4
\pages 63--74
\mathnet{http://mi.mathnet.ru/aa729}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1418255}
\zmath{https://zbmath.org/?q=an:0870.16023}
\transl
\jour St. Petersburg Math. J.
\yr 1997
\vol 8
\issue 4
\pages 585--592
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    • This publication is cited in the following 34 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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