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Type: Artigo de periódico
Title: Lie Algebras With Complex Structures Having Nilpotent Eigenspaces
Author: Santos E.C.L.
Martin L.A.B.S.
Abstract: Let (g, [·,]) be a Lie algebra with an integrable complex structure J. The ±i eigenspaces of J are complex subalgebras of gC isomorphic to the algebra (g, [*]J) with bracket [X * Y]J = 1/2 ([X, Y] - [JX, J Y]). We consider here the case where these subalgebras are nilpotent and prove that the original (g, [·,]) 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.
Rights: aberto
Identifier DOI: 
Date Issue: 2011
Appears in Collections:Unicamp - Artigos e Outros Documentos

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