On a Java library to perform S-expansions of Lie algebras
arXiv:1802.04468 · doi:10.1088/1742-6596/1085/5/052010
Abstract
The S-expansion method is a generalization of the Inönü-Wigner (IW) contraction that allows to study new non-trivial relations between different Lie algebras. Basically, this method combines a Lie algebra with a finite abelian semigroup in such a way that a new S-expanded algebra can be defined. When the semigroup has a zero-element and/or a specific decomposition, which is said to be resonant with the subspace structure of the original algebra, then it is possible to extract smaller algebras from which have interesting properties. Here we give a brief description of the S-expansion, its applications and the main motivations that lead us to elaborate a Java library, which automatizes this method and allows us to represent and to classify all possible S-expansions of a given Lie algebra.
arXiv comment7 pages, 1 figure, Talk at ACAT 2017, Seattle, USA, to appear in Proceedings of ACAT 2017
References in corpus (44)
- Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity
- Expanding Lie (super)algebras through abelian semigroups
- Standard General Relativity from Chern-Simons Gravity
- Wess-Zumino term for the AdS superstring and generalized Inonu-Wigner contraction
- Contractions of Low-Dimensional Lie Algebras
- Topological gravity and transgression holography
- Even-dimensional General Relativity from Born-Infeld gravity
- Gauged AdS-Maxwell algebra and gravity
- Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert lagrangian
- Chern-Simons and Born-Infeld gravity theories and Maxwell algebras type
- Generating infinite-dimensional algebras from loop algebras by expanding Maurer Cartan forms
- A generalized action for -dimensional Chern--Simons gravity
- N=1 Supergravity and Maxwell superalgebras
- Dynamical structure of Pure Lovelock gravity
- Maxwell Superalgebras and Abelian Semigroup Expansion
- Eleven-Dimensional Gauge Theory for the M Algebra as an Abelian Semigroup Expansion of osp(32|1)
- Pure Lovelock gravity and Chern-Simons theory
- Generalized Poincare algebras and Lovelock-Cartan gravity theory
- Dual Formulation of the Lie Algebra S-expansion Procedure
- Chern-Simons Supergravity in D=3 and Maxwell superalgebra
- New family of Maxwell like algebras
- Minimal AdS-Lorentz supergravity in three-dimensions
- General properties of the expansion methods of Lie algebras
- Lovelock gravities from Born-Infeld gravity theory
- Bianchi spaces and their 3-dimensional isometries as S-expansions of 2-dimensional isometries
- Generalized supersymmetric cosmological term in N=1 Supergravity
- AdS--Maxwell superalgebra and supergravity
- Inönü-Wigner Contraction and Supergravity
- On the Supersymmetric Extension of Gauss-Bonnet like Gravity
- Einstein-Hilbert action with cosmological term from Chern-Simons gravity
- Geometrical aspects of the Lie Algebra S-Expansion Procedure
- Generalized Galilean Algebras and Newtonian Gravity
- An Analytic Method for -Expansion involving Resonance and Reduction
- Infinite S-Expansion with Ideal Subtraction and Some Applications
- Resonant algebras and gravity
- Accelerated FRW Solutions in Chern-Simons Gravity
- S-Expansion of Higher-Order Lie Algebras
- Black hole for the Einstein-Chern-Simons gravity
- Generating Higher-Order Lie Algebras by Expanding Maurer Cartan Forms
- Lowest dimensional example on non-universality of generalized Inönü-Wigner contractions
- Static solutions in Einstein-Chern-Simons gravity
- Stellar equilibrium in Einstein-Chern-Simons gravity
- S-expansions of three-dimensional Lie algebras
- A Java library to perform S-expansions of Lie algebras