Fuzzy cylinders of finite length

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.