Cocalibrated structures on Lie algebras with a codimension one Abelian ideal
نویسندگان
چکیده
منابع مشابه
Abelian Complex Structures on Solvable Lie Algebras
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.
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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...
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The Nagano-Yagi-Goldmann theorem states that on the torus T, every affine (or projective) structure is invariant or is constructed on the basis of some Goldmann rings [N-Y]. It shows the interest to study the invariant affine structure on the torus T or on abelian Lie groups. Recently, the works of Kim [K] and Dekempe-Ongenae [D-O] precise the number of non equivalent invariant affine structure...
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ژورنال
عنوان ژورنال: Annals of Global Analysis and Geometry
سال: 2012
ISSN: 0232-704X,1572-9060
DOI: 10.1007/s10455-012-9326-0