Degenerations of Zinbiel and nilpotent Leibniz algebras

By Ivan Kaygorodov, Yury Popov, A. Pozhidaev, Y. Volkov. 2016

58 citations recorded by the source corpus.

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 varieties.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8da983d09f8c024656cbcd0441f079fd9970bff3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Y. Volkov
2. Ivan Kaygorodov

In Geometry and Topology

1. Y. Volkov
2. Ivan Kaygorodov

In Mathematical Physics

1. Y. Volkov
2. Ivan Kaygorodov

Citations in the corpus

• Degenerations of nilpotent algebras (2019, methodology): “This problem was solved for 2-dimensional pre-Lie algebras in [9], for 2-dimensional terminal algebras in [13], for 3-dimensional Novikov algebras in [10], for 3-dimensional Jordan algebras in [27], for 3-dimensional Jordan superalgebras in [6], for 3-dimensional Leibniz and 3-dimensional anticommut”
• The Variety of Two-dimensional Algebras Over an Algebraically Closed Field (2017, methodology): “For example, this problem was solved for two-dimensional pre-Lie algebras in [3], for three-dimensional Novikov algebras in [4], for four-dimensional Lie algebras in [7], for four-dimensional Zinbiel and nilpotent Leibniz algebras in [21], for nilpotent ûve- and six-dimensional Lie algebras in [15, ”