Expansions of algebras and superalgebras and some applications

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 Inonu-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).

Invited lecture delivered at the 'Deformations and Contractions in Mathematics and Physics Workshop', 15-21 January 2006, Mathematisches Forschungsinstitut Oberwolfach, Germany

References in corpus (2)

• Expanding Lie (super)algebras through abelian semigroups
• Non-Relativistic AdS Branes and Newton-Hooke Superalgebra

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• Three-dimensional non-relativistic extended supergravity with cosmological constant
• Generalized Maxwellian exotic Bargmann gravity theory in three spacetime dimensions
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• Three-dimensional exotic Newtonian supergravity theory with cosmological constant
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• An Analytic Method for $S$-Expansion involving Resonance and Reduction
• Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• Three-dimensional non-relativistic supergravity and torsion
• The Holographic c-theorem and Infinite-dimensional Lie Algebras
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• Extended Kinematical 3D Gravity Theories
• Non-relativistic gravity theories in four spacetime dimensions
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• Hietarinta Chern-Simons supergravity and its asymptotic structure