Abstract. Xu introduced a class of nongraded Hamiltonian Lie algebras. These Lie algebras have a Poisson bracket structure. In this paper, the isomorphism classes of these Lie algebras are determined by employing a “sandwich” method and by studying some features of these Lie algebras. It is obtained that two Hamiltonian Lie algebras are isomorphic if and only if their corresponding Poisson alge...

In this work we consider the moduli space of all noncommutative metric Lie algebras, having a nondegenerate symmetric invariant bilinear form, over $\mathbb C$ and R$ up to dimension 5 algebras in 6. We introduce cyclic reduced cohomology identify their deformations.

We show that the mapping cone of a morphism of differential graded Lie algebras χ : L → M can be canonically endowed with an L∞-algebra structure which at the same time lifts the Lie algebra structure on L and the usual differential on the mapping cone. Moreover, this structure is unique up to isomorphisms of L∞-algebras. The associated deformation functor coincides with the one introduced by t...

A Lie-admissible algebra gives a Lie algebra by anticommutativity. In this work we describe remarkable types of Lie-admissible algebras such as Vinberg algebras, pre-Lie algebras or Lie algebras. We compute the corresponding binary quadratic operads and study their duality. Considering Lie algebras as Lie-admissible algebras, we can define for each Lie algebra a cohomology with values in an Lie...

We define posets of types B, C, and D. These encode the matrix forms certain Lie algebras which lie between upper-triangular diagonal matrices. Our primary concern is index spectral theories such type-B, D poset algebras. For an important restricted class, we develop combinatorial formulas and, in particular, characterize corresponding to Frobenius In this latter case show that spectrum binary;...

A Lie group is, roughly speaking, an analytic manifold with a group structure such that the group operations are analytic. Lie groups arise in a natural way as transformation groups of geometric objects. For example, the group of all affine transformations of a connected manifold with an affine connection and the group of all isometries of a pseudo-Riemannian manifold are known to be Lie groups...

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

Abstract. This paper obtains all solvable 3-Lie algebras with the m-dimensional filiform 3-Lie algebra N (m ≥ 5) as a maximal hypo-nilpotent ideal, and proves that the m-dimensional filiform 3-Lie algebra N can’t be as the nilradical of solvable non-nilpotent 3-Lie algebras. By means of one dimensional extension of Lie algebras to the 3-Lie algebras, we get some classes of solvable Lie algebras...