Built on

Segal I E 1951 A class of operator algebras which are determined by groups Duke Math. J
1951
Earlier work this paper cites.
Inönü E and Wigner E P 1953 On the contraction of groups and their representations Proc. Nat. Acad. Sci. USA
1953
Earlier work this paper cites.
Inönü E 1964 Contractions of Lie groups and their representations Group theoretical concepts in elementary particle physics
1964
Earlier work this paper cites.
Weimar-Woods E 1995 Contractions of Lie algebras: generalized Inonu-Wigner contractions versus graded contractions J. Math. Phys
1995
Earlier work this paper cites.
Weimar-Woods E 2000 Contractions, generalized Inönü and Wigner contractions and deformations of finite-dimensional Lie algebras Rev. Math. Phys
2000
Earlier work this paper cites.
Hildebrant J 2001 Handbook of Finite Semigroup Programs LSU Mathematics Electronic Preprint Series
2001
Earlier work this paper cites.
Hatsuda M and Sakaguchi M 2003 Wess-Zumino term for the AdS superstring and generalized Inonu-Wigner contraction Prog. Theor. Phys
2003
Earlier work this paper cites.
de Azcarraga J A, Izquierdo J M, Picon M and Varela O 2003 Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity Nucl. Phys
2003
Earlier work this paper cites.
Izaurieta F, Rodriguez E and Salgado P 2006 Expanding Lie (super)algebras through Abelian semigroups J. Math. Phys
2006
Earlier work this paper cites.
Izaurieta F, Rodriguez E and Salgado P 2008 Eleven-dimensional gauge theory for the M algebra as an Abelian semigroup expansion of osp(32—1) Eur. Phys. J
2008
Earlier work this paper cites.
Izaurieta F, Rodriguez E, Perez A and Salgado P 2009 Dual Formulation of the Lie Algebra S-expansion Procedure J. Math. Phys
Original
2009
Earlier work this paper cites.
Caroca R, Merino N and Salgado P 2009 S-Expansion of Higher-Order Lie Algebras J. Math. Phys
Original
2009
Earlier work this paper cites.
Caroca R, Merino N, Perez A and Salgado P 2009 Generating Higher-Order Lie Algebras by Expanding Maurer Cartan Forms J. Math. Phys
Original
2009
Earlier work this paper cites.
Izaurieta F, Rodriguez E, Minning P, Salgado P and Perez A 2009 Standard General Relativity from Chern-Simons Gravity Phys. Lett
Original
2009
Earlier work this paper cites.
Soroka D V and Soroka V A 2009 Semi-simple extension of the (super)Poincare algebra Adv. High Energy Phys
2009
Earlier work this paper cites.
Caroca R, Merino N, Salgado P and Valdivia O 2011 Generating infinite-dimensional algebras from loop algebras by expanding Maurer-Cartan forms J. Math. Phys
2011
Earlier work this paper cites.

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Then

Concha P K, Fierro O, Rodríguez E K and Salgado P 2015 Chern-Simons supergravity in D = 3 D=3 and Maxwell superalgebra Phys. Lett
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2015
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Later among the works it cites.
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2018

On a Java library to perform S-expansions of Lie algebras

Inostroza, Carlos, Kondrashuk, Igor, Merino, Nelson et al.

Understand

The S-expansion method is a generalization of the In\"{o}n\"{u}-Wigner (IW) contraction that allows to study new non-trivial relations between different Lie algebras.

Basically, this method combines a Lie algebra $\mathcal{G}$ with a finite abelian semigroup $S$ in such a way that a new S-expanded algebra $\mathcal{G}_{S}$ 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 $\mathcal{G}_{S}$ 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.

Built on

Segal I E 1951 A class of operator algebras which are determined by groups Duke Math. J
1951
Earlier work this paper cites.
Inönü E and Wigner E P 1953 On the contraction of groups and their representations Proc. Nat. Acad. Sci. USA
1953
Earlier work this paper cites.
Inönü E 1964 Contractions of Lie groups and their representations Group theoretical concepts in elementary particle physics
1964
Earlier work this paper cites.
Weimar-Woods E 1995 Contractions of Lie algebras: generalized Inonu-Wigner contractions versus graded contractions J. Math. Phys
1995
Earlier work this paper cites.
Weimar-Woods E 2000 Contractions, generalized Inönü and Wigner contractions and deformations of finite-dimensional Lie algebras Rev. Math. Phys
2000
Earlier work this paper cites.
Hildebrant J 2001 Handbook of Finite Semigroup Programs LSU Mathematics Electronic Preprint Series
2001
Earlier work this paper cites.
Hatsuda M and Sakaguchi M 2003 Wess-Zumino term for the AdS superstring and generalized Inonu-Wigner contraction Prog. Theor. Phys
2003
Earlier work this paper cites.
de Azcarraga J A, Izquierdo J M, Picon M and Varela O 2003 Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity Nucl. Phys
2003
Earlier work this paper cites.
Izaurieta F, Rodriguez E and Salgado P 2006 Expanding Lie (super)algebras through Abelian semigroups J. Math. Phys
2006
Earlier work this paper cites.
Izaurieta F, Rodriguez E and Salgado P 2008 Eleven-dimensional gauge theory for the M algebra as an Abelian semigroup expansion of osp(32—1) Eur. Phys. J
2008
Earlier work this paper cites.
Izaurieta F, Rodriguez E, Perez A and Salgado P 2009 Dual Formulation of the Lie Algebra S-expansion Procedure J. Math. Phys
Original
2009
Earlier work this paper cites.
Caroca R, Merino N and Salgado P 2009 S-Expansion of Higher-Order Lie Algebras J. Math. Phys
Original
2009
Earlier work this paper cites.
Caroca R, Merino N, Perez A and Salgado P 2009 Generating Higher-Order Lie Algebras by Expanding Maurer Cartan Forms J. Math. Phys
Original
2009
Earlier work this paper cites.
Izaurieta F, Rodriguez E, Minning P, Salgado P and Perez A 2009 Standard General Relativity from Chern-Simons Gravity Phys. Lett
Original
2009
Earlier work this paper cites.
Soroka D V and Soroka V A 2009 Semi-simple extension of the (super)Poincare algebra Adv. High Energy Phys
2009
Earlier work this paper cites.
Caroca R, Merino N, Salgado P and Valdivia O 2011 Generating infinite-dimensional algebras from loop algebras by expanding Maurer-Cartan forms J. Math. Phys
2011
Earlier work this paper cites.