Algèbres de Lie et produit scalaire invariant

Médina, Alberto; Revoy, Philippe

doi:10.24033/asens.1496

Cited by 211 publications

(278 citation statements)

References 2 publications

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“…So we recover the result of Medina and Revoy in [4] obtained by describing the space Der a (g 2n+2 ) that b 2 = n 2 − 1.…”

Section: The Betti Numbers For a Family Of Solvable Quadratic Lie Algsupporting

confidence: 86%

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The Betti Numbers for a Family of Solvable Lie Algebras

Duong

2017

Bull. Malays. Math. Sci. Soc.

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ABSTRACT. We give a characterization of symplectic quadratic Lie algebras that their Lie algebra of inner derivations has an invertible derivation. A family of symplectic quadratic Lie algebras is introduced to illustrate this situation. Finally, we calculate explicitly the Betti numbers of a family of solvable Lie algebras in two ways: using the cohomology of quadratic Lie algebras and applying a Pouseele's result on extensions of the onedimensional Lie algebra by Heisenberg Lie algebras.

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“…So we recover the result of Medina and Revoy in [4] obtained by describing the space Der a (g 2n+2 ) that b 2 = n 2 − 1.…”

Section: The Betti Numbers For a Family Of Solvable Quadratic Lie Algsupporting

confidence: 86%

“…In Section 2, motivated by Corollary 4.4 in [4], we give the Betti numbers for a family of solvable quadratic Lie algebras defined as follows. For each n ∈ N, let g 2n+2 denote the Lie algebra with basis {X 0 , ..., X n ,Y 0 , ...,Y n } and non-zero Lie brackets…”

Section: I(xy Z) = B([xy ] Z) ∀ X Y Z ∈ Gmentioning

confidence: 99%

The Betti Numbers for a Family of Solvable Lie Algebras

Duong

2017

Bull. Malays. Math. Sci. Soc.

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“…We say that a Lie algebra with an invariant scalar product is indecomposable if it cannot be written as the direct product of two orthogonal ideals. A theorem of Medina and Revoy [10] (see also [12] for a refinement) says that an indecomposable (finite-dimensional) Lie algebra with an invariant scalar product is one of the following:…”

Section: Proof Formentioning

confidence: 99%

“…Thus if the double extension is to be indecomposable, then g must be abelian. In summary, an indecomposable lorentzian Lie algebra is either simple or a double extension of an abelian Lie algebra by a one-dimensional Lie algebra and hence solvable (see, e.g., [10]). …”

Section: Proof Formentioning

confidence: 99%

Plücker-type relations for orthogonal planes

Figueroa-O’Farrill

Papadopoulos

2004

Journal of Geometry and Physics

145

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Abstract. We explore a Plücker-type relation which occurs naturally in the study of maximally supersymmetric solutions of certain supergravity theories. This relation generalises at the same time the classical Plücker relation and the Jacobi identity for a metric Lie algebra and coincides with the Jacobi identity of a metric n-Lie algebra. In low dimension we present evidence for a geometric characterisation of the relation in terms of middle-dimensional orthogonal planes in euclidean or lorentzian inner product spaces.

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“…The classification problem for arbitrary signature looks very complicated and includes, for example, the classification of Lie algebras which admit a nondegenerate ad-invariant symmetric bilinear form. An inductive construction of solvable Lie algebras with such a form was given by V. Kac [K], see also [MR1], [Bo] and [MR2].…”

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confidence: 99%

Classification of indefinite hyper-Kähler symmetric spaces

Alekseevsky

Cortés

2001

Asian Journal of Mathematics

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Abstract. We classify indefinite simply connected hyper-Kahler symmetric spaces. Any such space without flat factor has commutative holonomy group and signature (4m,4ra). We establish a natural 1-1 correspondence between simply connected hyper-Kahler symmetric spaces of dimension 8m and orbits of the group GL(m, H) on the space (5 4 C n ). r of homogeneous quartic polynomials S in n = 2m complex variables satisfying the reality condition S = rS } where r is the real structure induced by the quaternionic structure of C 2m = ffiP. We define and classify also complex hyperKahler symmetric spaces. Such spaces without flat factor exist in any (complex) dimension divisible by 4.

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Algèbres de Lie et produit scalaire invariant

Cited by 211 publications

References 2 publications

The Betti Numbers for a Family of Solvable Lie Algebras

The Betti Numbers for a Family of Solvable Lie Algebras

Plücker-type relations for orthogonal planes

Classification of indefinite hyper-Kähler symmetric spaces

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