矩阵分解与五边形映射
Matrix factorizations and pentagon maps
AI总结：
本研究提出一类特殊矩阵，其分解问题等价于非交换变量下的多种五边形及Yang-Baxter映射，证明了2阶情形对应齐次归一化映射，3阶情形可得到该映射的扩展及新型缠绕类新映射。
摘要：
我们提出一类特殊的矩阵类，这类矩阵参与的分解问题等价于用非交换变量表示的常值及缠绕（非定常）五边形、反五边形或Yang-Baxter映射。具体而言，我们证明该类2阶矩阵的分解等价于齐次归一化映射。从3阶矩阵出发，我们得到了齐次归一化映射的一种扩展，以及全新的缠绕五边形、反五边形和Yang-Baxter映射。
英文摘要：
We propose a specific class of matrices which participate in factorization problems that turn to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon or Yang-Baxter maps, expressed in non-commutative variables. In detail, we show that factorizations of order $N=2$ matrices of this specific class are equivalent to the homogeneous normalization map. From order $N=3$ matrices, we obtain an extension of the homogeneous normalization map, as well as novel entwining pentagon, reverse-pentagon and Yang-Baxter maps.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
