直接和多边形和单纯形方程的格拉斯曼参数化解

A. Dimakis, I. Korepanov
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引用次数: 12

摘要

我们考虑多边形和单纯形方程,其中最简单的非平凡例子分别是五边形(5-gon)和Yang- Baxter(2-单纯形)。我们研究了向量空间直接和中的(2n+1)-gon和2n-单纯形方程的一般结构。然后,我们给出了它们的解的构造,用格拉斯曼方程Gr(n+1,2n+1)的元素参数化。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Grassmannian-parameterized solutions to direct-sum polygon and simplex equations
We consider polygon and simplex equations, of which the simplest nontrivial examples are pentagon (5-gon) and Yang--Baxter (2-simplex), respectively. We examine the general structure of (2n+1)-gon and 2n-simplex equations in direct sums of vector spaces. Then we provide a construction for their solutions, parameterized by elements of the Grassmannian Gr(n+1,2n+1).
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