# Degenerations of nilpotent associative commutative algebras

@article{Kaygorodov2019DegenerationsON, title={Degenerations of nilpotent associative commutative algebras}, author={Ivan Kaygorodov and Samuel A. Lopes and Yury Popov}, journal={Communications in Algebra}, year={2019}, volume={48}, pages={1632 - 1639} }

Abstract We give a complete description of degenerations of complex 5-dimensional nilpotent associative commutative algebras. As corollary, we have the description of all rigid algebras in the variety of 5-dimensional commutative Leibniz algebras.

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R A ] 2 J ul 2 02 1 The algebraic and geometric classification of nilpotent right alternative algebras 1

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#### References

SHOWING 1-10 OF 43 REFERENCES

Degenerations of nilpotent algebras

- Mathematics
- 2019

We give a complete description of degenerations of $3$-dimensional nilpotent algebras, $4$-dimensional nilpotent commutative algebras and $5$-dimensional nilpotent anticommutative algebras over $… Expand

Degenerations of binary Lie and nilpotent Malcev algebras

- Mathematics
- 2016

ABSTRACT We describe degenerations of four-dimensional binary Lie algebras, and five- and six-dimensional nilpotent Malcev algebras over ℂ. In particular, we describe all irreducible components of… Expand

Degenerations of Zinbiel and nilpotent Leibniz algebras

- Mathematics
- 2016

ABSTRACT We describe degenerations of four-dimensional Zinbiel and four-dimensional nilpotent Leibniz algebras over In particular, we describe all irreducible components in the corresponding… Expand

The classification of algebras of level two

- Mathematics
- 2015

Abstract This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the varieties of Jordan, Lie and… Expand

The algebraic and geometric classification of nilpotent Novikov algebras

- Mathematics
- Journal of Geometry and Physics
- 2019

Abstract This paper is devoted to the complete algebraic and geometric classification of 4-dimensional nilpotent Novikov algebras over ℂ .

The Variety of 7-Dimensional 2-Step Nilpotent Lie Algebras

- Computer Science, Mathematics
- Symmetry
- 2018

This note considers degenerations between complex 2-step nilpotent Lie algebras of dimension 7 within the variety N 7 2, whose closures give the irreducible components of the variety. Expand

Degenerations of Jordan Superalgebras

- Mathematics
- Bulletin of the Malaysian Mathematical Sciences Society
- 2018

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

The classification of algebras of level one

- Mathematics
- 2013

Abstract In the present paper we obtain a list of algebras, up to isomorphism, such that the closure of any complex finite-dimensional algebra contains one of the algebras of the given list.

The algebraic and geometric classification of nilpotent binary Lie algebras

- Mathematics, Computer Science
- Int. J. Algebra Comput.
- 2019

We give a complete algebraic classification of nilpotent binary Lie algebras of dimension at most 6 over an arbitrary field of characteristic not 2 and a complete geometric classification of… Expand

The Variety of Two-dimensional Algebras Over an Algebraically Closed Field

- Mathematics
- Canadian Journal of Mathematics
- 2019

Abstract The work is devoted to the variety of two-dimensional algebras over algebraically closed fields. First we classify such algebras modulo isomorphism. Then we describe the degenerations and… Expand