On Zinbiel and Tortkara superalgebras

2025/08/15 by Bouarroudj, Sofiane, Mashurov, Farukh · 1 citation
#17A30 #17A50 #17A70 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.11382

Abstract

In this paper, we study Zinbiel superalgebras and special Tortkara superalgebras, highlighting key differences between the super and the non-super setting. We present examples of Zinbiel superalgebras with Rota-Baxter operators and construct a basis for free Zinbiel superalgebras. Moreover, we establish a superalgebraic analogue of the Lie criterion for Zinbiel superalgebras. In contrast to the classical case, some homomorphic images of special Tortkara superalgebras on two generators are exceptional. Finally, we present a classification of all Tortkara superalgebras of dimensions 2 and 3.

Citations

• On the generalized Poisson and transposed Poisson algebras
• Algebras constructed by Rota-Baxter operators
• Hidden structures behind ambient symmetries of the Maurer-Cartan equation
• Zinbiel superalgebras
• A structure theorem for streamed information
• Zinbiel algebras are nilpotent
• Zinbiel algebras and multiple zeta values
• Areas of areas generate the shuffle algebra
• On tortkara triple systems

Cited by

• Flat pseudo-Euclidean Leibniz superalgebras

Related

• Zinbiel superalgebras
• Superalgebras with Homogeneous structures of Lie type
• Zinbiel bialgebras, relative Rota-Baxter operators and the related Yang-Baxter Equation
• Rota-Baxter Operators on pre-Lie superalgebras and beyond
• Abelian subalgebras and ideals of maximal dimension in Zinbiel algebras