Introduction to sh Lie algebras for physicists

TL;DR

This paper introduces sh Lie algebras, a generalization of Lie algebras arising in string field theory and higher spin physics, aiming to make their mathematical structure accessible to physicists.

Contribution

It explains the mathematical foundations of sh Lie algebras and their relevance to string field theory and physics, bridging the gap between abstract mathematics and physical applications.

Findings

Generalization of Lie algebra in string field theory

Connection to higher spin particles and constrained Hamiltonians

Accessible presentation of complex algebraic formulas

Abstract

Closed string field theory leads to a generalization of Lie algebra which arose naturally within mathematics in the study of deformations of algebraic structures. It also appeared in work on higher spin particles \cite{BBvD}. Representation theoretic analogs arose in the mathematical analysis of the Batalin-Fradkin-Vilkovisky approach to constrained Hamiltonians. A major goal of this paper is to see the relevant formulas, especially in closed string field theory, as a generalization of those for a differential graded Lie algebra, hopefully describing the mathematical essentials in terms accessible to {\it physicists}.