2020/10/27 by Mucyo Karemera, Karemera, Mucyo
Mathematics · #18M05 #20G42 #57K31 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:18M05 #msc:20G42 #msc:57K31
paper · pdf · doi:10.48550/arxiv.2010.14633
arXiv admin note: text overlap with arXiv:1008.3103 by other authors
openalex publication_date 2020/10/27 · arxiv created 2021/11/26 · arxiv updated 2021/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct quantum invariants of 3-manifolds based on a \mathfraksl3 matrix dilogarithm proposed by Kashaev. This matrix dilogarithm is an \mathfraksl3 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 \mathfraksl3 matrix dilogarithm can be considered as a 6j-symbol associated to modules of a quantum group related to Uq(\mathfraksl3). Moreover, we show that the quantum invariants aforementioned allow to define a \mathfraksl3 version of Kashaev's invariants, opening a route to define a \mathfraksl3 version of Baseilhac and Benedetti's quantum hyperbolic invariants.