Related papers: D\'erivations dans les alg\`ebres d'\'evolution \`…
The starting point of this work is that the class of evolution algebras over a fixed field is closed under tensor product. This arises questions about the inheritance of properties from the tensor product to the factors and conversely. For…
This thesis was concerned with classifying the real indecomposable solvable Lie algebras with codimension one nilradicals of dimensions two through seven. This thesis was organized into three chapters. In the first, we described the…
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…
In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be decomposed into the sum of a derivation and a center valued map. We extend some known results on the…
In this paper we prove that every irreducible representation of a Leibniz algebra can be obtained from irreducible representations of the semisimple Lie algebra from the Levi decomposition. We also prove that - in general - for (semi)simple…
We classify (possibly non commutative) algebras of low rank over a domain R. We first review results for algebras of rank 2 and for finite-dimensional division algebras over the real numbers. These results motivate us to consider which…
We construct all solvable Lie algebras with a specific n-dimensional nilradical n_{n,3} which contains the previously studied filiform nilpotent algebra n_{n-2,1} as a subalgebra but not as an ideal. Rather surprisingly it turns out that…
One of the questions investigated in deformation theory is to determine to which algebras can a given associative algebra be deformed. In this paper we investigate a different but related question, namely: for a given associative…
The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We give characterize multiplicative simple Hom-associative algebras and show some examples deforming the $2\times 2$-matrix algebra…
In the paper, we obtain the estimates connecting codimensions of varieties of non-associative algebras and corresponding varieties of dialgebras.
In this paper we investigate locally nilpotent derivations on the polynomial algebra in three variables over a field of characteristic zero. We introduce an iterating construction giving all locally nilpotent derivations of rank $2$. This…
In this paper we study decompositions and classification problems for unbounded derivations in Bunce-Deddens-Toeplitz and Bunce-Deddens algebras. We also look at implementations of these derivations on associated GNS Hilbert spaces.
In the present paper we prove the existence outer derivations finite-dimensional solvable Lie algebras with nilradical of maximal rank and complementary subspace to nilardical of dimension less than rank of the nilradical.
In the paper we describe the derivations of two $\mathbb{N}$-graded infinity-dimensional Lie algebras $\mathbf{n}_1$ and $\mathbf{n}_1$ what are positive parts of affine Kats-Moody algebras $A^{(1)}_1$ and $A^{(2)}_2$, respectively. Then we…
Hom-Lie algebras are generalizations of Lie algebras that arise naturally in the study of nonassociative algebraic structures. In this paper, the concepts of solvable and nilpotent Hom-Lie algebras studied further. In the theory of groups,…
In this paper we use key elements of the Olver's approach to Hamiltonian evolution equations in partial derivatives and propose an algebraic construction appropriate for Hamiltonian evolution systems with constraints.
The paper is devoted to the study of local derivations and automorphisms of nilpotent Lie algebras. Namely, we proved that nilpotent Lie algebras with indices of nilpotency $3$ and $4$ admit local derivation (local automorphisms) which is…
Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving…
For each $n\ge2$ we classify all $n$-dimensional algebras over an arbitrary infinite field which have the property that the $n$-dimensional abelian Lie algebra is their only proper degeneration.
In the present paper, local derivations and local automorphisms of five-dimensional naturally graded nilpotent associative algebras are studied. Namely, a general form of the matrices of local derivations and local automorphisms of algebras…