C*-algebras associated with Hilbert C*-quad modules of finite type

TL;DR

This paper constructs a universal C*-algebra from finite type Hilbert C*-quad modules with bimodule structures and finite bases, providing examples and establishing its universal property.

Contribution

It introduces a new method to construct C*-algebras from Hilbert C*-quad modules of finite type and proves their universality under specific relations.

Findings

Constructed C*-algebras from Hilbert C*-quad modules of finite type.

Proved the universality of these C*-algebras under certain relations.

Presented examples illustrating the construction and properties.

Abstract

A Hilbert $C^*$-quad module of finite type has a multi structure of Hilbert $C^*$-bimodules with two finite bases. We will construct a $C^*$-algebra from a Hilbert $C^*$-quad module of finite type and prove its universality subject to certain relations among generators. Some examples of the $C^*$-algebras from Hilbert $C^*$-quad modules of finite type will be presented.