On the SL(2,ℂ) quantum 6j-symbols and their relation to the hyperbolic volume

IF 1 2区数学 Q1 MATHEMATICS

Quantum Topology Pub Date : 2013-07-02 DOI:10.4171/QT/41

F. Costantino, J. Murakami

引用次数: 20

Abstract

We generalize the colored Alexander invariant of knots to an invariant of graphs and we construct a face model for this invariant by using the corresponding 6j -symbols, which come from the non-integral representations of the quantum group Uq.sl2/. We call it the SL.2; C/-quantum 6j -symbols, and show their relation to the hyperbolic volume of a truncated tetrahedron. Mathematics Subject Classification (2010). Primary 46L37; Secondary 46L54, 82B99.

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SL(2，)量子6j符号及其与双曲体积的关系

我们将结点的彩色Alexander不变量推广到图的不变量，并利用量子群Uq.sl2/的非积分表示中相应的6j -符号构造了该不变量的面模型。我们称之为sl - 2;C/-量子6j -符号，并展示了它们与截断四面体双曲体积的关系。数学学科分类(2010)。主要46 l37;二级46L54, 82B99。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.