Multibracket simple Lie algebras

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Abstract

We introduce higher-order (or multibracket) simple Lie algebras that generalize the ordinary Lie algebras. Their `structure constants' are given by Lie algebra cohomology cocycles which, by virtue of being such, satisfy a suitable generalization of the Jacobi identity. Finally, we introduce a nilpotent, complete BRST operator associated with the l multibracket algebras which are based on a given simple Lie algebra of rank l.

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Introduction to sh Lie algebras for physicists

Jim Stasheff, Tom Lada (1992)

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}.

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Publication date Created: 1996-11-26

Publication date Updated: 1996-11-27

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ArXiV ID: hep-th/9611220

SO-VID: ac40dc32-dde2-46a4-abc8-238b75a143d4

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Journal reference Group 21: Physical Applications and Mathematical Aspects of Geometry, Groups and Algebra, Vol I, pp. 103-107. World Sci. 1997

Comments Latex file; 5 pages. Some latex problems solved. Talk given at the XXI International Colloquium on Group Theoretical Methods in Physics. July 1996, Goslar, Germany. To appear in the Proceedings

Categories hep-th math.QA q-alg

ScienceOpen disciplines: High energy & Particle physics,Algebra

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ScienceOpen disciplines: High energy & Particle physics, Algebra

Multibracket simple Lie algebras

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