Lie algebras with complex structures having nilpotent eigenspaces
| Autor: | Luiz A. B. San Martin, Edson Carlos Licurgo Santos |
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| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
Discrete mathematics
Pure mathematics Hypercomplex number Integrable system General Mathematics Mathematics::Rings and Algebras Structure (category theory) Nilpotent Bracket (mathematics) complex structure Lie algebra Nilpotent and solvable Lie algebras Algebra over a field Nilpotent group Mathematics |
| Zdroj: | Proyecciones (Antofagasta), Volume: 30, Issue: 2, Pages: 247-263, Published: 2011 Proyecciones (Antofagasta) v.30 n.2 2011 SciELO Chile CONICYT Chile instacron:CONICYT |
| Popis: | 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] â [JX, JY]). 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. |
| Databáze: | OpenAIRE |
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