On explicit realization of algebra of complex divided powers of U_q(\mathfraksl(2))

2019/11/28 by Pavel Sultanich, Sultanich, Pavel
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1911.12902

openalex publication_date 2019/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove that the explicit realization of arbitrary complex powers of generators of quantum group U_q(\mathfraksl(2)) satisfies all the commutation relations of the algebra of complex powers, including the generalized Kac's identity which was announced in our previous paper. It turns out that the latter identity in this realization is equivalent to 6-9 integral identity on quantum dilogarithm.

Citations

• Current-Like Variables in Massive and Massless Integrable Models
• Liouville bootstrap via harmonic analysis on a noncompact quantum group

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