Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry)

L. Corwin; Y. Ne'eman; S. Sternberg

doi:10.1103/RevModPhys.47.573

Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry)

L. Corwin, Y. Ne'eman, and S. Sternberg

Rev. Mod. Phys. 47, 573 – Published 1 July 1975

Abstract

Graded Lie algebras have recently become a topic of interest in physics in the context of "supersymmetries," relating particles of differing statistics. In mathematics, graded Lie algebras have been known for some time in the context of deformation theory. In this paper we discuss basic properties of graded Lie algebras and present various new constructs for producing examples of such algebras. In addition we present a short survey of the role played by graded Lie algebras in mathematics and review in some detail the recent applications of supersymmetry in the physics of particles and fields.

DOI:https://doi.org/10.1103/RevModPhys.47.573

Authors & Affiliations

L. Corwin^*

Department of Mathematics, Yale University, New Haven, Connecticut 06520

Y. Ne'eman^† and S. Sternberg^‡

Department of Physics and Astronomy, Tel-Aviv University, Tel-Aviv, Israel

^*NSF Grant GP 30673 and Sloan Foundation Fellow.
^†Partially supported by the United States-Israel Binational Science Foundation.
^‡Partially supported by the National Science Foundation and the John Simon Guggenheim Foundation.