Weakening idempotency in K-theory

TL;DR

This paper introduces a relaxed approach to defining K-theory for C*-algebras, replacing strict idempotency conditions with weaker relations between matrices, potentially broadening the scope of K-theoretic analysis.

Contribution

It presents a novel framework for K-theory that uses less restrictive matrix relations, expanding the theoretical foundation of the subject.

Findings

K-theory can be defined with weaker matrix relations

Potential for broader applications in C*-algebra analysis

New theoretical insights into K-theoretic structures

Abstract

We show that the K-theory of C*-algebras can be defined by pairs of matrices satisfying less strict relations than idempotency.