1. On the algorithm to find S-related Lie algebras
- Author
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Felip Nadal, Nelson Merino, Carlos Inostroza, Igor Kondrashuk, AstroParticule et Cosmologie (APC (UMR_7164)), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), AstroParticule et Cosmologie ( APC - UMR 7164 ), Centre National de la Recherche Scientifique ( CNRS ) -Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Observatoire de Paris-Université Paris Diderot - Paris 7 ( UPD7 ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
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High Energy Physics - Theory ,History ,[ INFO ] Computer Science [cs] ,Java ,Computer science ,[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] ,group theory ,FOS: Physical sciences ,algebra: Lie ,02 engineering and technology ,01 natural sciences ,Education ,Lie algebra ,0202 electrical engineering, electronic engineering, information engineering ,FOS: Mathematics ,Order (group theory) ,[INFO]Computer Science [cs] ,Mathematics - Numerical Analysis ,0101 mathematics ,Abelian group ,numerical calculations ,Mathematical Physics ,computer.programming_language ,higher-order: 6 ,010102 general mathematics ,group: abelian ,Mathematical Physics (math-ph) ,Numerical Analysis (math.NA) ,Computational Physics (physics.comp-ph) ,16. Peace & justice ,Computer Science Applications ,Algebra ,High Energy Physics - Theory (hep-th) ,020201 artificial intelligence & image processing ,[ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph] ,computer ,Physics - Computational Physics - Abstract
In this article we describe the Java library that we have recently constructed to automatize the S-expansion method, a powerful mathematical technique allowing to relate different Lie algebras. An important input in this procedure is the use of abelian semigroups and thus, we start with a brief review about the classification of non-isomorphic semigroups made in the literature during the last decades, and explain how the lists of non-isomorphic semigroups up to order 6 can be used as inputs in many of the methods of our library. After describing the main features of the classes that compose our library we present a new method called fillTemplate which tuns out to be very useful to answer whether two given algebras can be S-related., Comment: 6 pages, Talk at ACAT 2017, Seattle, USA, to appear in Proceedings of ACAT 2017
- Published
- 2017
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