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Commutator algebras arising from splicing operations

100%
Sverchkov S.
Open Mathematics
|
2014
|
tom 12
|
nr 11
1687-1699
EN
We prove that the variety of Lie algebras arising from splicing operation coincides with the variety CM of centreby-metabelian Lie algebras. Using these Lie algebras we find the minimal dimension algebras generated the variety CM and the variety of its associative envelope algebras. We study the splicing n-ary operation. We show that all n-ary (n > 2) commutator algebras arising from this operation are nilpotent of index 3. We investigate the generalization of the splicing n-ary operation, and we formulate a series of open problems.
2
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A complete classification of four-dimensional paraKähler Lie algebras

100%
Calvaruso G.
Complex Manifolds
|
2015
|
tom 2
|
nr 1
EN
We consider paraKähler Lie algebras, that is, even-dimensional Lie algebras g equipped with a pair (J, g), where J is a paracomplex structure and g a pseudo-Riemannian metric, such that the fundamental 2-form Ω(X, Y) = g(X, JY) is symplectic. A complete classification is obtained in dimension four.
3
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Jacobi-Bernoulli cohomology and deformations of schemes and maps

88%
Ran Z.
Open Mathematics
|
2012
|
tom 10
|
nr 4
1541-1591
EN
We introduce a notion of Jacobi-Bernoulli cohomology associated to a semi-simplicial Lie algebra (SELA). For an algebraic scheme X over ℂ, we construct a tangent SELA J X and show that the Jacobi-Bernoulli cohomology of J X is related to infinitesimal deformations of X.
4
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The Hurwitz determinants and the signatures of irreducible representations of simple real Lie algebras

75%
Rudy A.
Open Mathematics
|
2005
|
tom 3
|
nr 4
606-613
EN
The paper deals with the real classical Lie algebras and their finite dimensional irreducible representations. Signature formulae for Hermitian forms invariant relative to these representations are considered. It is possible to associate with the irreducible representation a Hurwitz matrix of special kind. So the calculation of the signatures is reduced to the calculation of Hurwitz determinants. Hence it is possible to use the Routh algorithm for the calculation.
5
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Lie algebraic characterization of manifolds

51%
Grabowski J., Poncin N.
Open Mathematics
|
2004
|
tom 2
|
nr 5
811-825
EN
Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold is characterized by the corresponding Lie algebra of linear differential operators, i.e. isomorphisms of such Lie algebras are induced by the appropriate class of diffeomorphisms of the underlying manifolds.
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