Year: 2020
Type: preprint
Abstract: We construct quantum invariants of 3-manifolds based on a $\mathfrak{sl}_3$ matrix dilogarithm proposed by Kashaev. This matrix dilogarithm is an $\mathfrak{sl}_3$ analogue of the (cyclic) quantum dilogarithm used to define Kashaev's invariants as well as Baseilhac and Benedetti's quantum hyperbolic invariants. % In this article, we show that the $\mathfrak{sl}_3$ matrix dilogarithm can be considered as a 6$j$-symbol associated to modules of a quantum group related to $U_q(\mathfrak{sl}_3)$. Moreover, we show that the quantum invariants aforementioned allow to define a $\mathfrak{sl}_3$ version of Kashaev's invariants, opening a route to define a $\mathfrak{sl}_3$ version of Baseilhac and Benedetti's quantum hyperbolic invariants.
Source: arXiv (Cornell University)
Author: Karemera, Mucyo
Institution: Auburn University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3209090496