Banach半格代数的单同调与Hochschild上同调
Simplicial homology and Hochschild cohomology of Banach semilattice algebras
摘要：
半格的${\ell}^1$ -卷积代数在系数双模对称的情况下，具有1、2、3次平凡同调.我们把这个结果推广到所有具有对称系数的$\geq 1$次上同调群.我们的技术证明了一个更强的分裂结果，即分裂可以自然的基础半格。
英文摘要：
The ${\ell}^1$-convolution algebra of a semilattice is known to have trivial cohom ology in degrees 1,2 and 3 whenever the coefficient bimodule is symmetric. We ex tend this result to all cohomology groups of degree $\geq 1$ with symmetric coef ficients. Our techniques prove a stronger splitting result, namely that the spli tting can be made natural with respect to the underlying semilattice.
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