Abstract

We consider the reduced semigroup \(C^{*}\)-algebras for monoids with the cancellation property. If there exists a surjective semigroup homomorphism from a monoid onto a group then the corresponding semigroup \(C^{*}\)-algebra can be endowed with the structure of a Banach module over its \(C^{*}\)-subalgebra. For a such monoid, we give conditions under which this Banach module is free.

中文翻译：

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一个半群 $$\boldsymbol{C}^{\mathbf{*}}$$ -代数，它是一个自由 Banach 模

摘要

我们考虑具有取消性质的幺半群的约简半群\(C^{*}\) -代数。如果存在从幺半群到群的满射半群同态，那么对应的半群\(C^{*}\) -代数可以在其\(C^{*}\) - 上赋予 Banach 模的结构-子代数。对于这样的幺半群，我们给出了这个 Banach 模块是免费的条件。