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Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry). (English) Zbl 0557.17004
Summary: Graded Lie algebras have 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 constructions 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.

MSC:
17B70 Graded Lie (super)algebras
81T60 Supersymmetric field theories in quantum mechanics
17B81 Applications of Lie (super)algebras to physics, etc.
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