满足Zamolodchikov方程的非交换双有理映射与Desargues格
Non-commutative bi-rational maps satisfying Zamolodchikov equation, and Desargues lattices
摘要：
我们提出了新的解决方案的功能Zamolodchikov四面体方程的双有理映射在完全非交换变量。所有的映射都来自Desargues格，它提供了非阿贝尔Hirota-Miwa系统解的几何实现。第一个映射是使用原来的广田规相应的线性问题，第二个从其仿射（非齐次）描述。我们还提供了一个本地杨巴克斯特方程的方法内的地图的解释。我们利用第二个地图分解成两个更简单的地图，如我们所示，满足五边形条件。并给出了五边形映射间匹配十项条件的几何意义。在齐次坐标系中的Desargues格的一般描述允许定义Zamolodchikov方程的另一个解，但是具有应该以特定方式调整的功能参数。它的超局域约化产生了一个具有Zamolodchikov性质的双有理量子映射（具有两个中心参数），该映射保持Weyl对易关系。在经典极限下，我们构造了相应的满足Zamolodchikov条件的Poisson映射.
英文摘要：
We present new solutions of the functional Zamolodchikov tetrahedron equation in terms of birational maps in totally non-commutative variables. All the maps originate from Desargues lattices, which provide geometric realization of solutions to the non-Abelian Hirota-Miwa system. The first map is derived using the original Hirota's gauge for the corresponding linear problem, and the second one from its affine (non-homogeneous) description. We provide also an interpretation of the maps within the local Yang-Baxter equation approach. We exploit decomposition of the second map into two simpler maps which, as we show, satisfy the pentagonal condition. We provide also geometric meaning of the matching ten-term condition between the pentagonal maps. The generic description of Desargues lattices in homogeneous coordinates allows to define another solution of the Zamolodchikov equation, but with functional parameter which should be adjusted in a particular way. Its ultra-local reduction produces a birational quantum map (with two central parameters) with Zamolodchikov property, which preserves Weyl commutation relations. In the classical limit our construction gives the corresponding Poisson map satisfying the Zamolodchikov condition.
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