相关论文: Degenerations of nilpotent algebras

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

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…

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.

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 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 geometric classification of $n$-dimensional nilpotent, commutative nilpotent and anticommutative nilpotent algebras. We prove that the corresponding geometric varieties are irreducible, find their dimensions and describe explicit…

We describe degenerations of four-dimensional binary Lie algebras, and five- and six-dimensional nilpotent Malcev algebras over \mathbb{C}. In particular, we describe all irreducible components of these varieties.

We give a classification of $5$- and $6$-dimensional complex one-generated nilpotent bicommutative algebras.

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…

We classify the $4$-dimensional nilpotent bicommutative algebras over $\mathbb C$ from both algebraic and geometric approaches.

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…

This paper is devoted to the complete algebraic classification of complex $5$-dimensional nilpotent commutative algebras. Our method of classification is based on the standard method of classification of central extensions of smaller…

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

An algebraic classification of complex $5$-dimensional nilpotent commutative $\mathfrak{CD}$-algebras is given. This classification is based on an algebraic classification of complex $5$-dimensional nilpotent Jordan algebras.

We give the classification of $5$- and $6$-dimensional complex one-generated nilpotent assosymmetric algebras.

The paper is devoted to the description of the varieties of complex 5-dimensional nilpotent Jordan superalgebras. We find all representatives for the isomorphism classes, using the Jordan normal form, results of simultaneous matrix…

The paper is devoted to give a complete classification of five-dimension nilpotent evolution algebras over an algebraically closed field. We obtained a list of 27 isolated non-isomorphic nilpotent evolution algebras and 2 families of…

This paper is devoted to the complete algebraic classification of complex 5-dimensional nilpotent bicommutative algebras.

We give a geometric classification of complex $n$-dimensional $2$-step nilpotent (all, commutative and anticommutative) algebras. Namely, has been found the number of irreducible components and their dimensions. As a corollary, we have a…