Classification of the direct limits of involution simple associative algebras and the corresponding dimension groups

TL;DR

This paper classifies countable direct limits of finite dimensional involution simple associative algebras and their dimension groups using invariants like supernatural numbers and real parameters.

Contribution

It provides a complete classification of these algebras and their dimension groups, extending previous work to arbitrary characteristic fields.

Findings

Classification using two supernatural numbers and two real parameters

Complete description of the structure of direct limits of involution simple algebras

Corresponding classification of dimension groups

Abstract

A classification of (countable) direct limits of finite dimensional involution simple associative algebras over an algebraically closed field of arbitrary characteristic is obtained. This also classifies the corresponding dimension groups. The set of invariants consists of two supernatural numbers and two real parameters.