Related papers: Algebraically rigid real solvable Lie algebras

This work provides five explicit constructions of the exceptional Lie algebra $\mathfrak{e}_8$, based on its semisimple subalgebras of maximal rank. Each of these models is graded by an abelian group, namely, $\mathbb{Z}_4$, $\mathbb{Z}_5$,…

We completely characterize cosymplectic and $\alpha$-cosymplectic Lie algebras in terms of corresponding symplectic Lie algebras and suitable derivations on them. Several examples are given and classification results are obtained in…

In this paper, we define partially capable Lie superalgebra. As an application we classify all capable nilpotent Lie superalgebras of dimension less than equal to five.

We investigate symplectic nilpotent Lie groups with Lagrangian normal subgroups. We show that there exists a bijection between the isomorphism classes of nilpotent Lie groups with Lagrangian normal subgroups and the isomorphism classes of…

Two-dimensional real hyporeductive triple algebras (h.t.a.) are investigated. A classification of such algebras is presented. As a consequence, a classification of two-dimensional real Lie triple algebras (i.e. generalized Lie triple…

We give simple and unified proofs of the known stability and rigidity results for Lie algebras, Lie subalgebras and Lie algebra homomorphisms. Moreover, we investigate when a Lie algebra homomorphism is stable under all automorphisms of the…

We study the local Killing Lie algebra of meromorphic almost rigid geometric structures on complex manifolds. This leads to classification results for compact complex manifolds bearing holomorphic rigid geometric structures.

We call a finite-dimensional complex Lie algebra $\mathfrak{g}$ strongly rigid if its universal enveloping algebra $\Ug$ is rigid as an associative algebra, i.e. every formal associative deformation is equivalent to the trivial deformation.…

Lie superautomorphisms of prime associative superalgebras are considered. A definitive result is obtained for central simple superalgebras: their Lie superautomorphisms are of standard forms, except when the dimension of the superalgebra in…

We investigate the compatible root graded anti-pre-Lie algebraic structures on any finite-dimensional complex simple Lie algebra by the representation theory of ${\rm sl_2(\C)}$. We show that there does not exist a compatible root graded…

The paper concerns two versions of the notion of real forms of Lie superalgebras. One is the standard approach, where a real form of a complex Lie superalgebra is a real Lie superalgebra such that its complexification is the original…

This paper proves the isomorphic criterion theorem for (n+2)-dimensional n-Lie algebras, and gives a complete classification of (n+1)-dimensional n-Lie algebras and (n+2)-dimensional n-Lie algebras over an algebraically closed field of…

Some forms of Lie algebras of types E_6, E_7, and E_8 are constructed using the exterior cube of a rank 9 finitely generated projective module.

The author has previously shown that solvable Lie A-algebras and complemented solvable Lie algebras decompose as a vector space direct sum of abelian subalgebras, and their ideals relate nicely to this decomposition. However, neither of…

In this paper we classify irreducible integrable representations of loop toroidal Lie algebras with finite dimensional weight spaces. In both the cases we classify modules, when a part of center acts non-trivially and trivially on modules.

We present a local and constructive differential geometric description of finite-dimensional solvable and transitive Lie algebras of vector fields. We show that it implies a Lie's conjecture for such Lie algebras. Also infinite-dimensional…

The exceptional simple Lie algebras of types E7 and E8 are endowed with optimal $SL_2^n$-structures, and are thus described in terms of the corresponding coordinate algebras. These are nonassociative algebras which much resemble the so…

We establish an improved upper estimate on dimension of any solvable algebra s with its nilradical isomorphic to a given nilpotent Lie algebra n. Next we consider Levi decomposable algebras with a given nilradical n and investigate…

The $n$-Lie bialgebras are studied. In Section 2, the $n$-Lie coalgebra with rank $r$ is defined, and the structure of it is discussed. In Section 3, the $n$-Lie bialgebra is introduced. A triple $(L, \mu, \Delta)$ is an $n$-Lie bialgebra…

We prove that for each dimension not less than five there exists a contraction between solvable Lie algebras that can be realized only with matrices whose Euclidean norms necessarily approach infinity at the limit value of contraction…