Related papers: Lie structures and chain ideal lattices
The goal of this paper is to investigate a class of algebras called sandwich algebras, which are certain complex Lie algebras with a nilpotent radical whose elements are sandwiches. We present a classification of all very special sandwich…
Every Lie algebra over a field $E$ gives rise to new Lie algebras over any subfield $F \subseteq E$ by restricting the scalar multiplication. This paper studies the structure of these underlying Lie algebra in relation to the structure of…
The PostLie algebra is an enriched structure of the Lie algebra that has recently arisen from operadic study. It is closely related to pre-Lie algebra, Rota-Baxter algebra, dendriform trialgebra, modified classical Yang-Baxter equations and…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
Let $A$ be a unitary ring and let $(\mathbf{I(A),\subseteq })$ be the lattice of ideals of the ring $A.$ In this article we will study the property of the lattice $(\mathbf{I(A),\subseteq})$ to be Noetherian or not, for various types of…
Various questions on Lie ideals of C*-algebras are investigated. They fall roughly under the following topics: relation of Lie ideals to closed two-sided ideals; Lie ideals spanned by special classes of elements such as commutators,…
We investigate a connection between two important classes of Euclidean lattices: well-rounded and ideal lattices. A lattice of full rank in a Euclidean space is called well-rounded if its set of minimal vectors spans the whole space. We…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
Some cohomology classes associated with an ideal in a Lie algebra, a Poisson structure on the basic functions algebra of contact structure, its Poisson cohomology and geometric (pre)quantization are considered from the algebraic point of…
We study symplectic structures on filiform Lie algebras -- nilpotent Lie algebras of the maximal length of the descending central sequence. In the present article we classify the Lie algebras with the structure relations of the following…
We give an explicit description of the Lie algebra of derivations for a class of infinite dimensional algebras which are given by \'etale descent. The algebras under consideration are twisted forms of central algebras over rings, and…
We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and…
The main aim of this paper is to classify the distinct multiplicative Lie algebra structures (up to isomorphism) on a given group. We also see that for a given group $G$, every homomorphism from the non-abelian exterior square $G \wedge G$…
Divisible residuated lattices are algebraic structures corresponding to a more comprehensive logic than Hajek's basic logic with an important significance in the study of fuzzy logic. The purpose of this paper is to investigate commutative…
In this paper we study the lengths of certain chains of subalgebras of a Lie algebra L: namely, a chief series, a maximal chain of minimal length, a chain of maximal length in which each subalgebra is modular in L, and a chain of maximal…
We extend results related to maximal subalgebras and ideals from Lie to Leibniz algebras. In particular, we classify minimal non-elementary Leibniz algebras and Leibniz algebras with a unique maximal ideal. In both cases, there are types of…
We present a formalization, in the theorem prover Lean, of the classification of solvable Lie algebras of dimension at most three over arbitrary fields. Lie algebras are algebraic objects which encode infinitesimal symmetries, and as such…
Given a positive definite even lattice and a commutative ring, there is a standard construction of a lattice vertex algebra over the commutative ring, and it admits a natural grading by non-negative integers. We describe the groups of…
Thin Lie algebras are infinite-dimensional graded Lie algebras $L=\bigoplus_{i=1}^{\infty}$, with $\dim(L_1)=2$ and satisfying a covering property: for each $i$, each nonzero $z\in L_i$ satisfies $[zL_1]=L_{i+1}$. It follows that each…
Semiprime ideals of an arbitrary Leavitt path algebra L are described in terms of their generators. This description is then used to show that the semiprime ideals form a complete sublattice of the lattice of ideals of L, and they enjoy a…