Abelian Complex Structures on Solvable Lie Algebras
نویسندگان
چکیده
We obtain a characterization of the Lie algebras admitting abelian complex structures in terms of certain affine Lie algebras aff(A), where A is a commutative algebra.
منابع مشابه
Novikov Structures on Solvable Lie Algebras
We study Novikov algebras and Novikov structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov structure must be solvable. Conversely we present an example of a nilpotent 2-step solvable Lie algebra without any Novikov structure. We construct Novikov structures on certain Lie algebras via classical r-matrices and via extensions. In the latter case we lift No...
متن کاملAbelian Ideals of Maximal Dimension for Solvable Lie Algebras
We compare the maximal dimension of abelian subalgebras and the maximal dimension of abelian ideals for finite-dimensional Lie algebras. We show that these dimensions coincide for solvable Lie algebras over an algebraically closed field of characteristic zero. We compute this invariant for all complex nilpotent Lie algebras of dimension n ≤ 7. Furthermore we study the case where there exists an...
متن کاملSolvable Lie algebras with $N(R_n,m,r)$ nilradical
In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $N(R_n,m,r)$.We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.
متن کاملClassification of abelian complex structures on 6-dimensional Lie algebras
Let g be a Lie algebra, J an endomorphism of g such that J = −I , and let g be the ieigenspace of J in g := g ⊗R C. When g is a complex subalgebra we say that J is integrable, when g is abelian we say that J is abelian and when g is a complex ideal we say that J is bi-invariant. We note that a complex structure on a Lie algebra cannot be both abelian and biinvariant, unless the Lie bracket is t...
متن کاملThe Computation of Abelian Subalgebras in Low-Dimensional Solvable Lie Algebras
The main goal of this paper is to compute the maximal abelian dimension of each solvable nondecomposable Lie algebra of dimension less than 7. To do it, we apply an algorithmic method which goes ruling out non-valid maximal abelian dimensions until obtaining its exact value. Based on Mubarakzyanov and Turkowsky’s classical classifications of solvable Lie algebras (see [13] and [19]) and the cla...
متن کامل