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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
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
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
Linking options:
https://www.mathnet.ru/eng/aa729 https://www.mathnet.ru/eng/aa/v8/i4/p63
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