Related papers: The moduli space of 4-dimensional nilpotent comple…
The automorphisms of all 4-dimensional, real Lie Algebras are presented in a comprehensive way. Their action on the space of $4\times 4$, real, symmetric and positive definite, matrices, defines equivalence classes which are used for the…
The notion of symmetric Zinbiel superalgebras is introduced. We prove that the nilpotency index of a symmetric Zinbiel superalgebra is not greater than 4 and describe two-generated symmetric Zinbiel algebras and odd generated superalgebras.…
In this paper solvable Leibniz algebras with naturally graded non-Lie $p$-filiform $(n-p\geq4)$ nilradical and with one-dimensional complemented space of nilradical are described. Moreover, solvable Leibniz algebras with abelian nilradical…
This article is devoted to the classification of anti-dendriform algebras that are associated with associativity. They are characterized as algebras with two operations whose sum is associative. In particular, the paper is devoted to…
The index of a Lie algebra is an important invariant which arises in several areas, e.g. in the study of coadjoint orbits for a Lie group, in invariant theory and in representation theory. We study the index for several classes of nilpotent…
In this study, we classify some soliton nilpotent Lie algebras and possible candidates in dimension 8 and 9 up to isomorphy. We focus on 1 < 2 < ::: < n type of derivations where n is the dimension of the Lie algebras. We present algorithms…
Four-dimensional, oriented Lie algebras $\mathfrak{g}$ which satisfy the tame-compatible question of Donaldson for all almost complex structures $J$ on $\mathfrak{g}$ are completely described. As a consequence, examples are given of…
We construct large families of simple modules for untwisted affine Lie algebras using induction from one-dimensional modules over nilpotent loop subalgebras. We also show that the vector space of the first self-extensions for these module…
There are 6 types of 2-dimensional representations in general. For any groups and any monoids, we can construct the moduli of 2-dimensional representations for each type: the moduli of absolutely irreducible representations, representations…
We review the known results about characteristically nilpotent complex Lie algebras, as well as we comment recent developements in the theory.
A compatible associative algebra is a vector space equipped with two associative multiplication structures that interact in a certain natural way. This article presents the classification of these algebras with dimension less than four, as…
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 introduce a novel approach that employs techniques from noncommutative Poisson geometry to comprehend the algebra of invariants of two $n\times n$ matrices. We entirely solve the open problem of computing the algebra of invariants of two…
In this paper we study the Lie algebras of derivations of two-step nilpotent algebras. We obtain a class of Lie algebras with trivial center and abelian ideal of inner derivations. Among these, the relations between the complex and the real…
Throughout the current paper, we extend the study of Zinbiel algebras to Zinbiel superalgebras. In particular, we show that all the Zinbiel superalgebras over an arbitrary field are nilpotent in the same way as occurs for Zinbiel algebras.…
We discuss multi-graded nilpotent tuples of multi-graded vector spaces which are a generalization of graded nilpotent pairs. The multi-grading yields a natural notion of a shape of such tuple and our main interest is to answer the question…
We study commutative post-Lie algebras $(${\rm CPA}s$)$ from an algebraic point of view. Firstly, we find some new identities in {\rm CPA}, which shows that the commutative multiplication gives a medial and derived commutative associative…
We treat the topic of the closures of the nilpotent orbits of the Lie algebras of Exceptional groups through their descriptions as moduli spaces, in terms of Hilbert series and the highest weight generating functions for their…
In the present paper automorphisms, local and 2-local automorphisms of $n$-dimensional null-filiform and filiform associative algebras are studied. Namely, a common form of the matrix of automorphisms and local automorphisms of these…
We consider finite-dimensional complex Lie algebras admitting a periodic derivation, i.e., a nonsingular derivation which has finite multiplicative order. We show that such Lie algebras are at most two-step nilpotent and give several…