Abstract
After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras. Expanded (super)algebras have, in general, larger dimensions than the original algebra, but also include the İnönü–Wigner and generalized IW contractions as a particular case. As an example of a physical application of expansions, we discuss the relation between the possible underlying gauge symmetry of eleven-dimensional supergravity and the superalgebra osp(1|32).
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Invited lecture delivered at the Deformations and Contractions in Mathematics and Physics Workshop, 15–21 January 2006, Mathematisches Forschungsinstitut Oberwolfach (Germany).
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de Azcárraga, J.A., Izquierdo, J.M., Picón, M. et al. Expansions of Algebras and Superalgebras and Some Applications. Int J Theor Phys 46, 2738–2752 (2007). https://doi.org/10.1007/s10773-007-9385-3
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DOI: https://doi.org/10.1007/s10773-007-9385-3