Cohomology of idempotent braidings with applications to factorizable monoids
Cohomology of idempotent braidings with applications to factorizable monoids
复制标题
幂等编织的上同调及其在可分解幺半群中的应用
DOI：
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发表时间：
2016
影响因子：
0.8
通讯作者：
V. Lebed
中科院分区：
文献类型：
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作者：
V. Lebed
我们发展了计算么半群的Hochschild(Co)同调的新方法，它可以表示为Yang-Baxter方程的幂等集论解的结构么半群。它们包括自由的和对称的么半群；可分解的么半群，对于它，我们找到了关于直积的kunneth公式的推广；以及平台么半群。我们的关键结果是通过显式量子对称化映射确定了所讨论的(Co)同调与潜在的ybe解的同调。这部分回答了Farinati-Garcia-Galofre和Dilian Yang的问题。我们还得到了关于一般ybe解的(上)同调的新的结构结果。
We develop new methods for computing the Hochschild (co)homology of monoids which can be presented as the structure monoids of idempotent set-theoretic solutions to the Yang–Baxter equation. These include free and symmetric monoids; factorizable monoids, for which we find a generalization of the Kunneth formula for direct products; and plactic monoids. Our key result is an identification of the (co)homologies in question with those of the underlying YBE solutions, via the explicit quantum symmetrizer map. This partially answers questions of Farinati–Garcia-Galofre and Dilian Yang. We also obtain new structural results on the (co)homology of general YBE solutions.