The cyclic and simplicial cohomology of the Cuntz semigroup algebra
The cyclic and simplicial cohomology of the Cuntz semigroup algebra
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DOI：
10.1016/j.jmaa.2011.08.050
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发表时间：
2010-07
影响因子：
1.3
通讯作者：
Fr'ed'eric Gourdeau;M. White
中科院分区：
文献类型：
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作者：
Fr'ed'eric Gourdeau;M. White
本文的主要目的是确定Cuntz半群代数1（Sm）的简单和循环上同群。我们还确定了Banach空间中张量代数的简单和循环上同调，该类包含了m-生成器上的自由半群上的代数。为了做到这一点，我们首先建立了一些一般的结果，这些结果可用于研究一般的Banach代数的简单和循环上同。然后我们将注意力转向1(Sm)，表明n度的循环上同群在n为奇数时消失，并且在n为偶数（n大于等于2）时是一维的。使用Connes-Tzygan精确序列，这些结果用于显示n度的简单上同群在n大于或等于1时消失。一个类似的策略被用于巴拿赫空间的张量代数。
The main objective of this paper is to determine the simplicial and cyclic cohomology groups of the Cuntz semigroup algebra ℓ1(Sm). We also determine the simplicial and cyclic cohomology of the tensor algebra of a Banach space, a class which includes the algebra on the free semigroup on m-generators ℓ1(FSm). In order to do so, we first establish some general results which can be used when studying simplicial and cyclic cohomology of Banach algebras in general. We then turn our attention to ℓ1(Sm), showing that the cyclic cohomology groups of degree n vanish when n is odd and are one-dimensional when n is even (n⩾2). Using the Connes–Tzygan exact sequence, these results are used to show that the simplicial cohomology groups of degree n vanish for n⩾1. A similar strategy is used for the tensor algebra of a Banach space.