Related papers: Characterizing Nilpotent Associative Algebras by T…
We study codimension growth of infinite dimensional Lie algebras over a field of characteristic zero. We prove that if a Lie algebra $L$ is an extension of a nilpotent algebra by a finite dimensional semisimple algebra then the PI-exponent…
We compare the maximal dimension of abelian subalgebras and the maximal dimension of abelian ideals for finite-dimensional Lie algebras. We show that these dimensions coincide for solvable Lie algebras over an algebraically closed field of…
In this paper we obtain the classification of $p$-nilpotent restricted Lie algebras of dimension at most four over a perfect field of characteristic p.
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
We extend results on finite dimensional nilpotent Lie algebras to Leibniz algebras and counterexamples to others are found. One generator algebras are used in these examples and are investigated further.
In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the…
We classify the nilpotent Lie algebras of real dimension eight and minimal center that admit a complex structure. Furthermore, for every such nilpotent Lie algebra $\mathfrak{g}$, we describe the space of complex structures on…
Basic definitions and properties of nearly associative algebras are described. Nearly associative algebras are proved to be Lie-admissible algebras. Two-dimensional nearly associative algebras are classified, and its main classes are…
We describe a method for classifying the Novikov algebras with a given associated Lie algebra. Subsequently we give the classification of the Novikov algebras of dimension 3 over R and C, as well as the classification of the 4-dimensional…
The present article is part of a research program the aim of which is to find all indecomposable solvable extensions of a given class of nilpotent Lie algebras. Specifically in this article we consider a nilpotent Lie algebra n that is…
In this paper, we introduce the concept of relative Lie central extension for pair of multiplicative Lie algebras. Then, we discuss the concept of isoclinism for relative Lie central extensions and prove some related results. We also define…
We study the minimal dimension of solvable and nilpotent Lie algebras over a field of characteristic zero with given derived length $k$. This is motivated by questions on nildecomposable Lie algebras $\Lg=\La+\Lb$, arising in the context of…
Recently there has been considerable interest in studying the length and the depth of finite groups, algebraic groups and Lie groups. In this paper we introduce and study similar notions for algebras. Let $k$ be a field and let $A$ be an…
We investigate Lie algebras whose Lie bracket is also an associative or cubic associative multiplication to characterize the class of nilpotent Lie algebras with a nilindex equal to 2 or 3. In particular we study the class of 2-step…
Nilpotent Leibniz algebras with isomorphic maximal subalgebras are considered. The algebras are classified for coclass zero, one, and two. The results are field dependent.
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…
We study infinite-dimensional analogues of nilpotent and solvable Lie algebras, focusing on the classes of pro-nilpotent, residually nilpotent, pro-solvable and residually solvable Lie algebras. We extend classical triangularization results…
The structure of nilpotent symplectic algebras of maximal class has been studied in [8, 5]. In this paper, we study the dual subclass of algebras of minimal class. In particular, we show that symplectic alternating algebras of dimension up…
In this note we study associative dialgebras proving that the most interesting such structures arise precisely when the algebra is not semiprime. In fact the presence of some "perfection" property (simpleness, primitiveness, primeness or…
We describe an algorithm to compute the Schur multipliers of all nilpotent Lie $p$-rings in the family defined by a symbolic nilpotent Lie $p$-ring. Symbolic nilpotent Lie $p$-rings can be used to describe the isomorphism types of…