Non-commutative gauge symmetry from strong homotopy algebras

TL;DR

This paper constructs an L-infinity algebra framework for U(1) gauge transformations on non-commutative and non-associative spaces, integrating matter fields and exploring P-infinity algebra extensions.

Contribution

It provides an explicit L-infinity algebra formulation for non-commutative gauge symmetries, including matter fields and potential P-infinity algebra generalizations.

Findings

Explicit L-infinity algebra for U(1) gauge transformations on non-commutative spaces

Incorporation of matter fields as L-infinity modules

Discussion of P-infinity algebra extensions

Abstract

We explicitly construct an L$_\infty$ algebra that defines U$_{\star}(1)$ gauge transformations on a space with an arbitrary non-commutative and even non-associative star product. Matter fields are naturally incorporated in this scheme as L$_\infty$ modules. Some possibilities for including P$_\infty$ algebras are also discussed.