Related papers: Degenerations of nilalgebras

We give the full description of all degenerations of complex five dimensional noncommutative Heisenberg algebras. As a corollary, we have the full description of all degenerations of four dimensional anticommutative $3$-ary algebras.

We give a complete description of degenerations of complex $5$-dimensional nilpotent associative commutative algebras.

We describe all degenerations of three dimensional anticommutative algebras $\mathfrak{Acom}_3$ and of three dimensional Leibniz algebras $\mathfrak{Leib}_3$ over $\mathbb{C}.$ In particular, we describe all irreducible components and rigid…

We give a complete description of degenerations of $3$-dimensional nilpotent algebras, $4$-dimensional nilpotent commutative algebras and $5$-dimensional nilpotent anticommutative algebras over $ \mathbb C$. In particular, we correct…

We describe degenerations of three-dimensional Jordan superalgebras over $\mathbb{C}$. In particular, we describe all irreducible components in the corresponding varieties.

We determine the complete degeneration picture inside the variety of nilpotent associative algebras of dimension 3 over an algebraically closed field of characteristic not equal to 2. Comparing with the discussion in [Ivanova N.M. and…

The algebraic and geometric classification of all complex $3$-dimensional transposed Poisson algebras is obtained. Also, we discuss strong special $3$-dimensional transposed Poisson algebras.

We classify hom-Lie structures with nilpotent twisting map on $3$-dimensional complex Lie algebras, up to isomorphism, and classify all degenerations in such family. The ideas and techniques presented here can be easily extrapolated to…

$n$-ary algebras of the first degeneration level are described. A detailed classification is given in the cases $n=2,3$.

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…

We describe all degenerations of the variety $\mathfrak{Jord}_3$ of Jordan algebras of dimension three over $\mathbb{C}.$ In particular, we describe all irreducible components in $\mathfrak{Jord}_3.$ For every $n$ we define an…

A complete classification of a class of $3$-dimensional algebras is provided. In algebraically closed field $\mathbb{F}$ case this class is an open, dense (in Zariski topology) subset of $\mathbb{F}^{27}$.

We describe degenerations of four-dimensional Zinbiel and four-dimensional nilpotent Leibniz algebras over C. In particular, we describe all irreducible components in the corresponding varieties.

An algebraic deformation theory of coalgebra morphisms is constructed.

The work is devoted to the variety of $2$-dimensional algebras over an algebraically closed field. Firstly, we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of principal algebra series in the…

We provide a complete classification of three-dimensional associative algebras over the real and complex number fields based on a complete elementary proof. We list up all the multiplication tables of the algebras up to isomorphism. We…

In this work nul-filiform and filiform Zinbiel algebras are described up to isomorphism. Moreover, the classification of complex Zinbiel algebras is extended from dimensions $\leq 3$ up to the dimension $4.$

An algebraic deformation theory of dialgebra morphisms is obtained.

In this paper we study subalgebras of complex finite dimensional evolution algebras. We obtain the classification of nilpotent evolution algebras whose any subalgebra is an evolution subalgebra with a basis which can be extended to a…

We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.