带半群代数的单上同调
Simplicial cohomology of band semigroup algebras
摘要：
建立了卷积代数$\ell^1(S)$的单纯平凡性，其中$S$是带半群.这推广了第一作者[Glasgow Math. J. 2005，Houston J. Math. 2010]的结果。为了做到这一点，我们证明了这个代数的循环上同调在所有奇数度为零，并同构于$\ell^1(S)$上的连续迹空间的偶数度。我们的方法的关键是使用的结构半格的$S$，和相关的分级的$S$，连同一个归纳规范化程序在循环上同调，后者的技术似乎是新的，其基本策略可能适用于其他卷积代数的兴趣。
英文摘要：
We establish simplicial triviality of the convolution algebra $\ell^1(S)$, where $S$ is a band semigroup. This generalizes results of the first author [Glasgow Math. J. 2005, Houston J. Math. 2010]. To do so, we show that the cyclic cohomology of this algebra vanishes in all odd degrees, and is isomorphic in even degrees to the space of continuous traces on $\ell^1(S)$. Crucial to our approach is the use of the structure semilattice of $S$, and the associated grading of $S$, together with an inductive normalization procedure in cyclic cohomology; the latter technique appears to be new, and its underlying strategy may be applicable to other convolution algebras of interest.
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