Symmetric Zinbiel superalgebras

Abstract

The notion of symmetric Zinbiel superalgebras is introduced. We prove that the nilpotency index of a symmetric Zinbiel superalgebra is not greater than 4 and describe two-generated symmetric Zinbiel algebras and odd generated superalgebras. We discuss identities of mono and binary symmetric Zinbiel and Leibniz algebras. It is proven that each quadratic Zinbiel algebra is 2-step nilpotent. Also, we study double extensions of symmetric Zinbiel algebras.

References in corpus (9)

• Degenerations of Zinbiel and nilpotent Leibniz algebras
• Non-associative central extensions of null-filiform associative algebras
• Classification of bilinear maps with radical of codimension 2
• Time-warping invariants of multidimensional time series
• Cup-product for equivariant Leibniz cohomology and zinbiel algebras
• The algebraic and geometric classification of Zinbiel algebras
• Classification of regular parametrized one-relation operads
• Central extensions of 3-dimensional Zinbiel algebras
• A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn's formula