On a Classification of Irreducible Almost Commutative Geometries III

TL;DR

This paper extends the classification of irreducible, almost commutative geometries with non-degenerate spectral actions to include internal algebras with four simple summands, advancing the mathematical understanding of such geometries.

Contribution

It introduces a broader classification framework for irreducible, almost commutative geometries by considering internal algebras with four simple summands, expanding previous work.

Findings

Extended classification to include four simple summands

Identified conditions for non-degenerate spectral actions

Provided new mathematical structures for geometries

Abstract

We extend a classification of irreducible, almost commutative geometries whose spectral action is dynamically non-degenerate to internal algebras that have four simple summands.