Degenerations of Filippov algebras

Abstract

We consider the variety of Filippov ($n$-Lie) algebra structures on an $(n+1)$-dimensional vector space. The group $G{L}_n(K)$ acts on it, and we study the orbit closures with respect to the Zariski topology. This leads to the definition of Filippov algebra degenerations. We present some fundamental results on such degenerations, including trace invariants and necessary degeneration criteria. Finally, we classify all orbit closures in the variety of complex $(n+1)$-dimensional Filippov $n$-ary algebras.

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Cited by in corpus (7)

• Degenerations of nilpotent algebras
• The algebraic and geometric classification of nilpotent terminal algebras
• Transposed Poisson structures
• The geometric classification of nilpotent algebras
• The algebraic and geometric classification of nilpotent left-symmetric algebras
• The geometric classification of nilpotent $\mathfrak{CD}$-algebras
• The algebraic and geometric classification of nilpotent right alternative algebras