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arXiv · 2309.04721

Fuzzy cylinders of finite length

Andreas Sykora
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Abstract

We introduce non-commutative algebras, which can be associated with the function algebra of functions on a finite or half-finite cylinder. The algebras, which depend on a deformation parameter, are crossed product algebras of a partial group action of $\mathbb{Z}$ on an interval of the real line $\mathbb{R}$. Discrete representations of the algebras can be seen as matrix regularizations of the respective function algebra on the finite or half-finite cylinder and therefore as fuzzy space. In a second part of the article, we review crossed product algebras based on partial group actions and derive the results needed in the first part.

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Andreas Sykora. 2023-09-09. Fuzzy cylinders of finite length. https://arxiv.org/abs/2309.04721

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