The algebraic and geometric classification of nilpotent left-symmetric algebras

Abstract

This paper is devoted to the complete algebraic and geometric classification of complex $4$-dimensional nilpotent left-symmetric algebras. The corresponding geometric variety has dimension $15$ and decomposes into $3$ irreducible components determined by the Zariski closures of two one-parameter families of algebras and a two-parameter family of algebras (see Theorem B). In particular, there are no rigid $4$-dimensional complex nilpotent left symmetric algebras.

arXiv admin note: substantial text overlap with arXiv:1912.02691, arXiv:1812.01442, arXiv:2004.03598, arXiv:1902.01706

References in corpus (3)

• Field Algebras
• Bijective 1-cocycles and classification of 3-dimensional Left-symmetric Algebras
• Degenerations of Filippov algebras

Cited by in corpus (1)

• Non-associative algebraic structures: classification and structure