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Locally conformal symplectic structures on Lie algebras of type i and their solvmanifolds
(De Gruyter, 2019-05-01)
We study Lie algebras of type I, that is, a Lie algebra g where all the eigenvalues of the operator ad X are imaginary for all X g. We prove that the Morse-Novikov cohomology of a Lie algebra of type I is trivial for any ...
Jordan-Chevalley decomposition in lie algebras
(Canadian Mathematical Soc, 2019-06)
We prove that if is a solvable Lie algebra of matrices over a field of characteristic § and A∈s, then the semisimple and nilpotent summands of the Jordan-Chevalley decomposition of A belong to s if and only if there exist ...
On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras
(Canadian Mathematical Soc, 2014-12)
We describe of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field ...
Automorphisms of non-singular nilpotent Lie algebras
(Heldermann Verlag, 2013-03)
For a real, non-singular, 2-step nilpotent Lie algebra n, the group Aut(n)/ Aut0(n), where Aut0(n) is the group of automorphisms which act trivially on the center, is the direct product of a compact group with the 1-dimensional ...
There are no rigid filiform Lie algebras of low dimension
(Heldermann Verlag, 2019-01)
We prove that there are no rigid complex filiform Lie algebras in the variety of (filiform) Lie algebras of dimension less than or equal to 11. More precisely we show that in any Euclidean neighborhood of a filiform Lie ...
Free 2-step nilpotent Lie algebras and indecomposable representations
(Taylor & Francis, 2018-07)
Given an algebraically closed field F of characteristic 0 and an F-vector space V, let L(V) = V⊕Λ2(V) denote the free 2-step nilpotent Lie algebra associated to V. In this paper, we classify all uniserial representations ...
On the Hopf algebra structure of the lusztig quantum divided power algebrasSur la structure d’algèbre de Hopf des algèbres de puissances divisées quantiques de lusztig
(Universite Clermont Auvergne, 2020-03-09)
We study the Hopf algebra structure of Lusztig’s quantum groups. First we show that the zero part is the tensor product of the group algebra of a finite abelian group with the enveloping algebra of an abelian Lie algebra. ...
Comparison morphisms between two projective resolutions of monomial algebras
(Unión Matemática Argentina, 2017-07)
We construct comparison morphisms between two well-known projective resolutions of a monomial algebra A : the bar resolution Bar A and Bardzell’s resolution Ap A ; the first one is used to define the cup product and the ...
Vaisman solvmanifolds and relations with other geometric structures
(International Press Boston, 2020-02)
We characterize unimodular solvable Lie algebras with Vaisman structures in terms of Kahler flat Lie algebras equipped with a suitable derivation. Using this characterization we obtain algebraic restrictions for the existence ...
Classification of finite irreducible modules over the Lie Conformal Superalgebra CK 6
(Springer, 2013-01)
We classify all continuous degenerate irreducible modules over the exceptional linearly compact Lie superalgebra E(1, 6), and all finite degenerate irreducible modules over the exceptional Lie conformal superalgebra CK6, ...