论文标题
美元
$\mathfrak{sl}_3$ Matrix Dilogarithm as a $6j$-Symbol
论文作者
论文摘要
我们基于$ \ mathfrak {sl} _3 $ matrix dilogarithm构建3个manifolds的量子不变性。该矩阵差异是一种$ \ mathfrak {sl} _3 $（循环）量子diologarithm的模拟，用于定义Kashaev的不变性以及baseilhac和Benedetti的量子量表屈曲。 ％在本文中，我们表明$ \ mathfrak {sl} _3 $矩阵dilogarithm可以被视为与$ u_q（\ mathfrak {sl} _3）$相关的量子组模块相关的6 $ j $ symbol。此外，我们表明，上述量子不变符允许定义Kashaev的不变式的$ \ Mathfrak {Sl} _3 $版本，开了一条路由来定义$ \ Mathfrak {SL} _3 $ baseilhac和Benedetti的量子量子量子超级BOLIDBILIC INVARIANTS的版本。
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.
