Geodesic
The Heisenberg double and the pentagon relation
Algebra i analiz, Tome 8 (1996) no. 4, pp. 63-74.

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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. 
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     title = {The {Heisenberg} double and the pentagon relation},
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R. M. Kashaev. The Heisenberg double and the pentagon relation. Algebra i analiz, Tome 8 (1996) no. 4, pp. 63-74. http://geodesic.mathdoc.fr/item/AA_1996_8_4_a2/