Lie algebras with complex structures having nilpotent eigenspaces

Let (g,[Â·,Â·]) be a Lie algebra with an integrable complex structure J. The Â±i eigenspaces of J are complex subalgebras of gC isomorphic to the algebra (g,[*]J) with bracket [X * Y]J = 1/2 ([X,Y] â [JX, JY]). We consider here the case where these subalgebras are nilpotent and prove that the orig...

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Autores principales:	Licurgo Santos,Edson Carlos, San Martin,Luiz A. B
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2011
Materias:	Nilpotent and solvable Lie algebras complex structure
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000200008
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spelling	oai:scielo:S0716-091720110002000082014-11-05Lie algebras with complex structures having nilpotent eigenspacesLicurgo Santos,Edson CarlosSan Martin,Luiz A. B Nilpotent and solvable Lie algebras complex structure Let (g,[Â·,Â·]) be a Lie algebra with an integrable complex structure J. The Â±i eigenspaces of J are complex subalgebras of gC isomorphic to the algebra (g,[]J) with bracket [X Y]J = 1/2 ([X,Y] â [JX, JY]). We consider here the case where these subalgebras are nilpotent and prove that the original (g,[Â·,Â·]) Lie algebra must be solvable. We consider also the 6-dimensional case and determine explicitly the possible nilpotent Lie algebras (g,[]J). Finally we produce several examples illustrating different situations, in particular we show that for each given s there exists g with complex structure J such that (g,[]J) is s-step nilpotent. Similar examples of hypercomplex structures are also built.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.30 n.2 20112011-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000200008en10.4067/S0716-09172011000200008
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Nilpotent and solvable Lie algebras complex structure
spellingShingle	Nilpotent and solvable Lie algebras complex structure Licurgo Santos,Edson Carlos San Martin,Luiz A. B Lie algebras with complex structures having nilpotent eigenspaces
description	Let (g,[Â·,Â·]) be a Lie algebra with an integrable complex structure J. The Â±i eigenspaces of J are complex subalgebras of gC isomorphic to the algebra (g,[]J) with bracket [X Y]J = 1/2 ([X,Y] â [JX, JY]). We consider here the case where these subalgebras are nilpotent and prove that the original (g,[Â·,Â·]) Lie algebra must be solvable. We consider also the 6-dimensional case and determine explicitly the possible nilpotent Lie algebras (g,[]J). Finally we produce several examples illustrating different situations, in particular we show that for each given s there exists g with complex structure J such that (g,[]J) is s-step nilpotent. Similar examples of hypercomplex structures are also built.
author	Licurgo Santos,Edson Carlos San Martin,Luiz A. B
author_facet	Licurgo Santos,Edson Carlos San Martin,Luiz A. B
author_sort	Licurgo Santos,Edson Carlos
title	Lie algebras with complex structures having nilpotent eigenspaces
title_short	Lie algebras with complex structures having nilpotent eigenspaces
title_full	Lie algebras with complex structures having nilpotent eigenspaces
title_fullStr	Lie algebras with complex structures having nilpotent eigenspaces
title_full_unstemmed	Lie algebras with complex structures having nilpotent eigenspaces
title_sort	lie algebras with complex structures having nilpotent eigenspaces
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2011
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000200008
work_keys_str_mv	AT licurgosantosedsoncarlos liealgebraswithcomplexstructureshavingnilpotenteigenspaces AT sanmartinluizab liealgebraswithcomplexstructureshavingnilpotenteigenspaces
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Lie algebras with complex structures having nilpotent eigenspaces

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