幂等辫的上同调及其在可因子分解幺半群上的应用
Cohomology of idempotent braidings, with applications to factorizable monoids
摘要：
我们发展了计算幺半群的Hochschild（上）同调的新方法，这些幺半群可以表示为杨-巴克斯特方程的幂等集论解的结构幺半群。这些包括自由和对称的幺半群;可因子分解的幺半群，对于它，我们找到了直积的K{ü}nneth公式的推广;和platic幺半群。我们的主要结果是识别的（共）同源性的问题与那些潜在的YBE解决方案，通过明确的量子对称映射。这部分回答了Farinati-Garc{í}a-Galofre和Dilian Yang的问题。我们还获得了新的结构结果的（上）同调的一般YBE解决方案。
英文摘要：
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 K{ü}nneth 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--Garc{í}a-Galofre and Dilian Yang. We also obtain new structural results on the (co)homology of general YBE solutions.
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。
