Related papers: Five-dimensional nilpotent evolution algebras
This paper is devoted to give the complete algebraic and geometric classification of $4$-dimensional nilpotent Novikov algebras over $\mathbb C.$
In this paper we investigate the derivations of filiform Leibniz algebras. Recall that the set of filiform Leibniz algebras of fixed dimension is decomposed into three non-intersected families. We found sufficient conditions under which…
In this paper, we classify (n+5)-dimensional nilpotent n-Lie algebras of class two over the arbitrary field, when $n\ge 3$.
We study the varieties of Lie algebra laws and their subvarieties of nilpotent Lie algebra laws. We classify all degenerations of (almost all) five-step and six-step nilpotent seven-dimensional complex Lie algebras. One of the main tools is…
In this paper we classify filiform associative algebras of degree $k$ over a field of characteristic zero. Moreover, we also classify naturally graded complex filiform and quasi-filiform nilpotent associative algebras which are described by…
The paper is devoted to give the complete algebraic classification of nilpotent binary Lie algebras of dimension $\leq 6$ over an arbitrary base field ${\mathbb{F}}$ of characteristic not $2$ and the complete geometric classification of…
We classify the four dimensional perfect non-simple evolution algebras over a field having characteristic different from 2 and in which there are roots of orders 2, 3 and 7.
We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.
This work classifies three-dimensional simple evolution algebras over arbitrary fields. For this purpose, we use tools such as the associated directed graph, the moduli set, inductive limit group, Zariski topology and the dimension of the…
We classify all $6$-dimensional nilpotent Tortkara algebras over $\mathbb C.$
In this paper, we study modularity in the context of evolution algebras. Although this property has been previously considered, a complete description is still missing in several natural settings. In particular, we obtain a full…
In math.DG/0312243 we developed a general classification scheme for metric Lie algebras, i.e. for finite-dimensional Lie algebras equipped with a non-degenerate invariant inner product. Here we determine all nilpotent Lie algebras l with…
We give a geometric classification of all $6$-dimensional nilpotent Tortkara algebras over $\mathbb C$
First we describe the Skjelbred-Sund method for classifying nilpotent Lie algebras. Then we use it to classify 6-dimensional nilpotent Lie algebras over any field of characteristic not 2. The proof of this classification is essentially…
In this paper we give the complete classification of $5$-dimensional complex solvable symmetric Leibniz algebras.
The paper presents a subclass of the class of MD5-algebras and MD5-groups, i.e. five dimensional solvable Lie algebras and Lie groups such that their orbits in the co-adjoint representation (K-orbits) are orbits of zero or maximal…
We classify the non-degenerate two-step nilpotent Lie algebras of dimension 8 over the field of real numbers, using known results over complex numbers. We write explicit structure constants for these real Lie algebras.
To use evolution algebras to model population dynamics that both allow extinction and introduction of certain gametes in finite generations, nilpotency must be built into the algebraic structures of these algebras with the entire algebras…
The article presents the structure of the automorphism groups of two types of non-nilpotent Leibniz algebras with a dimension of 3.
We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. We study basic properties of the algebra. This algebra is…