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.
Holonomy braidings, biquandles and quantum invariants of links with $SL_2(\mathbb C)$ flat connections
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
R. Kashaev and N. Reshetikhin introduced the notion of holonomy braiding extending V. Turaev's homotopy braiding to describe the behavior of cyclic representations of the unrestricted quantum group $U_qsl_2$ at root of unity. In this paper, using quandles and biquandles we develop a general theory for Reshetikhin-Turaev ribbon type functor for tangles with quandle representations. This theory applies to the unrestricted quantum group $U_qsl_2$ and produces an invariant of links with a gauge class of quandle representations.
fields
math.QA 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
The holonomy braiding for $\mathcal{U}_\xi(\mathfrak{sl}_2)$ in terms of geometric quantum dilogarithms
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.