Related papers: One-generated nilpotent assosymmetric algebras
We classify all $6$-dimensional nilpotent Tortkara algebras over $\mathbb C.$
This paper is devoted to the complete algebraic and geometric classification of complex $5$-dimensional nilpotent binary Leibniz and $4$-dimensional nilpotent mono Leibniz algebras. As a corollary, we have the complete algebraic and…
This paper is devoted to the complete algebraic and geometric classification of complex $5$-dimensional nilpotent Leibniz algebras. In particular, the variety of complex $5$-dimensional nilpotent Leibniz algebras has dimension $24$ it has…
This study focuses on the analysis of derivations, centroids, and inner derivations of 5-dimensional complex nilpotent associative algebras. It presents the classification of these algebras of dimension less than five, as well as the…
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 give a geometric classification of complex $5$-dimensional nilpotent commutative $\mathfrak{CD}$-algebras. The corresponding geometric variety has dimension $24$ and decomposes into $10$ irreducible components determined by the Zariski…
This paper is devoted to give the complete algebraic and geometric classification of $4$-dimensional nilpotent Novikov algebras over $\mathbb C.$
This paper is devoted to the complete algebraic and geometric classification of complex $4$-dimensional nilpotent left-symmetric algebras. The corresponding geometric variety has dimension $15$ and decomposes into $3$ irreducible components…
We give a full classification of 6-dimensional nilpotent Lie algebras over an arbitrary field, including fields that are not algebraically closed and fields of characteristic~2. To achieve the classification we use the action of the…
For each complex 8-dimensional filiform Lie algebra we find another non isomorphic Lie algebra that degenerates to it. Since this is already known for nilpotent Lie algebras of rank $\ge 1$, only the caracteristically nilpotent ones should…
We present algebraic and geometric classifications of the $4$-dimensional complex nilpotent right alternative algebras. Specifically, we find that, up to isomorphism, there are only $9$ non-isomorphic nontrivial nilpotent right alternative…
The paper is devoted to classify nilpotent Jordan algebras of dimension up to five over an algebraically closed field of characteristic not 2. We obtained a list of 35 isolated non-isomorphic 5-dimensional nilpotent non-associative Jordan…
We develop a structure theory for nilpotent symplectic alternating algebras. We then give a classification of all nilpotent symplectic alternating algebras of dimension up to 10 over any field. The study reveals a new subclasses of powerful…
In this paper we study the varieties of nilpotent Lie superalgebras of dimension $\leq 5$. We provide the algebraic classification of these superalgebras and obtain the irreducible components in every variety. As a by product we construct…
This paper is a contribution to the development of the non associative algebras theory. More precisely, this work deals with the classification of the complex 4-dimensional Leibniz algebras. Note that the classification of 4-dimensional…
The geometric classifications of complex $4$-dimensional nilpotent Lie-Yamaguti algebras, $4$-dimensional nilpotent Bol algebras, and $4$-dimensional nilpotent compatible Lie algebras are given.
This paper is devoted to the complete algebraic and geometric classification of complex $4$-dimensional nilpotent weakly associative, complex $4$-dimensional symmetric Leibniz algebras, and complex $5$-dimensional nilpotent symmetric…
The type and several invariant subspaces related to the upper annihilating series of finite-dimensional nilpotent evolution algebras are introduced. These invariants can be easily computed from any natural basis. Some families of nilpotent…
In this paper, nilpotent n-Lie algebras of dimension n + 3 as well as nilpotent n-Lie algebras of class 2 and dimension n + 4 are classified.
In this paper, we classify (n+5)-dimensional nilpotent n-Lie algebras of class two over the arbitrary field, when $n\ge 3$.