论文标题
模块化组的投影表示
A Projective Representation of the Modular Group
论文作者
论文摘要
量子Teichmuller理论通过映射从非交通式圆环的表示的映射类组的映射类群的映射组的射击表示形式分配了不变性。在这里，我们专注于最简单的非共同圆环的表示，该代表依赖于圆环的映射类组的所有元素，$ sl_2（\ m athbb {z}）$。也称为模块化组。我们使用此表示形式将矩阵与$ sl_2（\ mathbb {z}）$的每个元素相关联;然后，我们计算关联矩阵的迹线和决定因素。
Quantum Teichmuller theory assigns invariants to three-manifolds via projective representations of mapping class groups derived from the representation of a noncommutative torus. Here, we focus on a representation of the simplest non-commutative torus which remains fixed by all elements of the mapping class group of the torus, $SL_2(\mathbb{Z})$. Also known as the modular group. We use this representation to associate a matrix to each element of $SL_2(\mathbb{Z})$; we then compute the trace and determinant of the associated matrix.
