Fuzzy cylinders of finite length

TL;DR

This paper introduces non-commutative algebraic models for finite and half-finite cylinders, providing fuzzy space regularizations and exploring their algebraic structures via partial group actions.

Contribution

It constructs new fuzzy space models for cylinders using crossed product algebras from partial group actions, linking algebraic structures with geometric regularizations.

Findings

Discrete representations serve as matrix regularizations of cylinder function algebras

The algebraic framework models fuzzy spaces of finite and half-finite cylinders

Provides a review of crossed product algebras based on partial group actions

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.