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).

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

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• Expanding Lie (super)algebras through abelian semigroups
• Wess-Zumino term for the AdS superstring and generalized Inonu-Wigner contraction
• The geometry of branes and extended superspaces
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Cited by in corpus (54)

• Lie Algebra Expansions and Actions for Non-Relativistic Gravity
• Maxwell Superalgebras and Abelian Semigroup Expansion
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• Dual Formulation of the Lie Algebra S-expansion Procedure
• Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra
• Extended $D=3$ Bargmann supergravity from a Lie algebra expansion
• Minimal AdS-Lorentz supergravity in three-dimensions
• Three-dimensional Maxwellian extended Bargmann supergravity
• General properties of the expansion methods of Lie algebras
• Carrollian and Non-relativistic Jackiw-Teitelboim Supergravity
• Three-Dimensional Extended Lifshitz, Schrödinger and Newton-Hooke Supergravity
• Bianchi spaces and their 3-dimensional isometries as S-expansions of 2-dimensional isometries
• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
• More on the Hidden Symmetries of 11D Supergravity
• Galilean free Lie algebras
• Three-dimensional exotic Newtonian gravity with cosmological constant
• Inönü-Wigner Contraction and $D=2+1$ Supergravity
• Three-dimensional non-relativistic extended supergravity with cosmological constant
• The algebraic structure of Galilean superconformal symmetries
• Generalized Maxwellian exotic Bargmann gravity theory in three spacetime dimensions
• Einstein-Hilbert action with cosmological term from Chern-Simons gravity
• Three-dimensional Poincaré supergravity and $\mathcal{N}$-extended supersymmetric BMS${}_3$ algebra
• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
• On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions
• Three-dimensional exotic Newtonian supergravity theory with cosmological constant
• Supersymmetrization Schemes of D=4 Maxwell Algebra
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• Geometrical aspects of the Lie Algebra S-Expansion Procedure
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• An Analytic Method for $S$-Expansion involving Resonance and Reduction
• Infinite S-Expansion with Ideal Subtraction and Some Applications
• Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• Three-dimensional non-relativistic supergravity and torsion
• Sources for Chern-Simons theories
• Three-Dimensional Higher-Order Schrödinger Algebras and Lie Algebra Expansions
• The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements
• S-Expansion of Higher-Order Lie Algebras
• Contractions of Filippov algebras
• Generating Higher-Order Lie Algebras by Expanding Maurer Cartan Forms
• New particle model in extended space-time and covariantization of planar Landau dynamics
• The Holographic c-theorem and Infinite-dimensional Lie Algebras
• Extended Kinematical 3D Gravity Theories
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• Non-relativistic gravity theories in four spacetime dimensions
• Non-Relativistic Four Dimensional p-Brane Supersymmetric Theories and Lie Algebra Expansion
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
• Local supersymmetric extensions of the Poincare and AdS invariant gravity
• BPS preons and the AdS-M-algebra
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• A Java library to perform S-expansions of Lie algebras
• Contractions from $osp(1|32)\oplus osp(1|32)$ to the M-theory superalgebra extended by additional fermionic generators
• Hietarinta Chern-Simons supergravity and its asymptotic structure
• Bosonic D=11 supergravity from a generalized Chern-Simons action