Perturbation semigroup of matrix algebras

TL;DR

This paper investigates the structure of the perturbation semigroup related to matrix algebras within noncommutative geometry, providing explicit computations for all matrix cases and extending the understanding of algebraic perturbations.

Contribution

It explicitly characterizes the perturbation semigroup for all matrix algebras, expanding the algebraic framework in noncommutative geometry.

Findings

Computed the perturbation semigroup for all matrix algebras

Extended the algebraic understanding of inner perturbations

Linked the semigroup to the unitary elements of the algebra

Abstract

In this article we analyze the structure of the semigroup of inner perturbations in noncommutative geometry. This perturbation semigroup is associated to a unital associative *-algebra and extends the group of unitary elements of this *-algebra. We compute the perturbation semigroup for all matrix algebras.