Exceptional fuzzy spaces and octonions

TL;DR

This paper constructs fuzzy spaces derived from the three non-trivial co-adjoint orbits of the exceptional Lie group G2, expanding the understanding of non-commutative geometries associated with exceptional symmetries.

Contribution

It introduces a novel construction of fuzzy spaces based on G2's co-adjoint orbits, which has not been explored before.

Findings

Explicit models of fuzzy spaces for G2 orbits

New insights into non-commutative geometry related to exceptional groups

Potential applications in theoretical physics and quantum geometry

Abstract

We construct the fuzzy spaces based on the three non-trivial co-adjoint orbits of the exceptional simple Lie group, $G_2$.