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A link invariant from quantum dilogarithm. (English) Zbl 1022.81574

Summary: The link invariant, arising from the cyclic quantum dilogarithm via the particular \(R\)-matrix construction is proved to coincide with the invariant of triangulated links in \(S^3\) introduced in [the author, Mod. Phys. Lett. A 9, No. 40, 3757–3768 (1994; Zbl 1015.17500)]. The obtained invariant, like Alexander-Conway polynomial, vanishes on disjoint union of links. The \(R\)-matrix can be considered as the cyclic analog of the universal \(R\)-matrix associated with \(U_q(sl(2))\) algebra.

MSC:

81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
33D80 Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics
57M25 Knots and links in the \(3\)-sphere (MSC2010)

Citations:

Zbl 1015.17500
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