The algebraic and geometric classification of Zinbiel algebras

Abstract

This paper is devoted to the complete algebraic and geometric classification of complex $5$-dimensional Zinbiel algebras. In particular, we proved that the variety of complex $5$-dimensional Zinbiel algebras has dimension $24$, it is defined by $16$ irreducible components and it has $11$ rigid algebras.

arXiv admin note: substantial text overlap with arXiv:2205.00444. substantial text overlap with arXiv:2106.00336, arXiv:1912.02691, arXiv:1812.01442, arXiv:2004.03598

References in corpus (3)

• The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras
• Central extensions of 3-dimensional Zinbiel algebras
• Naturally graded Zinbiel algebras with nilindex $n-3$

Cited by in corpus (4)

• The algebraic and geometric classification of transposed Poisson algebras
• Symmetric Zinbiel superalgebras
• Fundamental Theorems of Calculus and Zinbiel Algebras
• The algebraic and geometric classification of derived Jordan and bicommutative algebras