The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras

Abstract

This paper is devoted to the complete algebraic and geometric classification of complex $4$-dimensional nilpotent weakly associative, complex $4$-dimensional symmetric Leibniz algebras, and complex $5$-dimensional nilpotent symmetric Leibniz algebras. In particular, we proved that the variety of complex $4$-dimensional symmetric Leibniz algebras has no Vergne--Grunewald--O'Halloran Property (there is an irreducible component formed by only nilpotent algebras), but on the other hand, it has Vergne Property (there are no rigid nilpotent algebras).

arXiv commentarXiv admin note: substantial text overlap with arXiv:2106.00336, arXiv:1912.02691, arXiv:1812.01442, arXiv:2109.00483

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Cited by in corpus (5)

• The algebraic and geometric classification of transposed Poisson algebras
• Non-associative algebraic structures: classification and structure
• Transposed Poisson structures
• The algebraic and geometric classification of Zinbiel algebras
• Solvable Leibniz superalgebras whose nilradical has the characteristic sequence $(n-1,1\mid m)$ and nilindex $n+m$