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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References

SHOWING 1-10 OF 43 REFERENCES
Degenerations of nilpotent algebras
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
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 ofExpand
Degenerations of Zinbiel and nilpotent Leibniz algebras
ABSTRACT We describe degenerations of four-dimensional Zinbiel and four-dimensional nilpotent Leibniz algebras over In particular, we describe all irreducible components in the correspondingExpand
The classification of algebras of level two
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 andExpand
The algebraic and geometric classification of nilpotent Novikov algebras
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
TLDR
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
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
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
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 ofExpand
The Variety of Two-dimensional Algebras Over an Algebraically Closed Field
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 andExpand
...
1
2
3
4
5
...