Operator algebras associated to modules over an integral domain

TL;DR

This paper introduces a new operator algebra constructed from modules over an integral domain using the Fock semicrossed product, and explores its properties as a model for semicrossed products.

Contribution

It defines a novel operator algebra associated with modules over an integral domain and analyzes its $C^*$-envelope and properties.

Findings

The $C^*$-envelope of the semicrossed product is characterized.

Properties of these algebras as models for semicrossed products are studied.

The approach provides new insights into operator algebras related to algebraic structures.

Abstract

We use the Fock semicrossed product to define an operator algebra associated to a module over an integral domain. We consider the $C^*$-envelope of the semicrossed product, and then consider properties of these algebras as models for studying general semicrossed products.