Spectra of locally matrix algebras

TL;DR

This paper characterizes the spectra of locally matrix algebras, providing a comprehensive classification and a new proof of a key theorem, with applications to embedding problems.

Contribution

It offers a complete description of spectra for locally matrix algebras and introduces a novel proof of the Dixmier-Baranov Theorem.

Findings

All possible spectra of locally matrix algebras are classified.

A new proof of the Dixmier-Baranov Theorem is provided.

Applications to embeddings of locally matrix algebras are demonstrated.

Abstract

We describe spectra of associative (not necessarily unital and not necessarily countable-dimensional) locally matrix algebras. We determine all possible spectra of locally matrix algebras and give a new proof of Dixmier-Baranov Theorem. As an application of our description of spectra we determine embeddings of locally matrix algebras.