Related papers: Contact Lie poset algebras
A coassociative Lie algebra is a Lie algebra equipped with a coassociative coalgebra structure satisfying a compatibility condition. The enveloping algebra of a coassociative Lie algebra can be viewed as a coalgebraic deformation of the…
We extend the notion of connection in order to be able to study singular geometric structures, namely, we consider a notion of connection on a Lie algebroid which is a natural extension of the usual concept of connection. Using connections,…
In this paper we show that the set of closure relations on a finite poset P forms a supersolvable lattice, as suggested by Rota. Furthermore this lattice is dually isomorphic to the lattice of closed sets in a convex geometry (in the sense…
We define hypersymplectic structures on Lie algebroids recovering, as particular cases, all the classical results and examples of hypersymplectic structures on manifolds. We prove a 1-1 correspondence theorem between hypersymplectic…
We determine all the contractions within the class of finite-dimensional real Lie algebras whose coadjoint orbits have dimensions $\le2$.
We define a general notion of abstract double Lie algebroid. We show (1) that the double Lie algebroid of a double Lie groupoid is a double Lie algebroid in this sense; (2) that the double cotangent constructed from Lie algebroid structures…
The notion of a matched pair of Lie algebras was introduced in the study of Lie bialgebras and Poisson-Lie groups. In this paper, we introduce representations and cohomology of a matched pair of Lie algebras. We show that there is a…
Let g be a simplicial Lie algebra with Moore complex Ng of length k. Let G be the simplicial Lie group integrating g, which is simply connected in each simplicial level. We use the 1-jet of the classifying space of G to construct, starting…
The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…
We investigate Lie bialgebra structures on simple Lie algebras of non-split type $A$. It turns out that there are several classes of such Lie bialgebra structures, and it is possible to classify some of them. The classification is obtained…
For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation…
The algebra generated by the down and up operators on a differential partially ordered set (poset) encodes essential enumerative and structural properties of the poset. Motivated by the algebras generated by the down and up operators on…
The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analyzed, and their generalized Casimir invariants calculated. It is shown that rank one solvable…
We characterize the structure of a seven-dimensional Lie algebra with non-trivial center endowed with a closed G$_2$-structure. Using this result, we classify all unimodular Lie algebras with non-trivial center admitting closed…
Infinitesimal symmetries of $S^1$-bundle gerbes are modelled with multiplicative vector fields on Lie groupoids. It is shown that a connective structure on a bundle gerbe gives rise to a natural horizontal lift of multiplicative vector…
The present paper contains a systematic study of the structure of metric Lie algebras, i.e., finite-dimensional real Lie algebras equipped with a non-degenerate invariant symmetric bilinear form. We show that any metric Lie algebra without…
A coset relation algebra is one embeddable into some full coset relation algebra, the latter is an algebra constructed from a system of groups, a coordinated system of isomorphisms between quotients of these groups, and a system of cosets…
In the note some construction of Lie algebras is introduced. It is proved that the construction has the same property as a well known wreath product of groups [1]: Any extension of groups can be embedded into their wreath product [2].
We define hom-Lie algebroids, a definition that may seem cumbersome at first, but which is justified, first, by a one-to-one corespondence with hom-Gerstenhaber algebras, a notion that we also introduce, and several examples, including…
Motivated by Kohno's result on the holonomy Lie algebra of a hyperplane arrangement, we define the holonomy Lie algebra of a finite geometric lattice in a combinatorial way. For a solvable pair of lattices, we show that the holonomy Lie…