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arxiv: q-alg/9503005 · v1 · pith:3MZWTH3Znew · submitted 1995-03-14 · q-alg · math.QA

Heisenberg Double and Pentagon Relation

R.M. Kashaev This is my paper
classification q-alg math.QA
keywords relationdoublepentagonheisenbergsolutionsalgebrascanonicalconstant
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It is shown that the Heisenberg double has a canonical element, satisfying the pentagon relation. From a given invertible constant solution to the pentagon relation one can restore the structure of the underlying algebras. Drinfeld double can be realized as a subalgebra in the tensor square of the Heisenberg double. This enables one to write down solutions to the Yang-Baxter relation in terms of solutions to the pentagon relation.

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  1. The holonomy braiding for $\mathcal{U}_\xi(\mathfrak{sl}_2)$ in terms of geometric quantum dilogarithms

    math.QA 2025-09 unverdicted novelty 5.0

    Derives explicit factorization of the holonomy R-matrix for U_ξ(sl₂) at a root of unity into four geometric quantum dilogarithms satisfying a holonomy Yang-Baxter equation.