On Zinbiel and Tortkara superalgebras
Rings and Algebras
2025-08-18 v1
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.
Keywords
Cite
@article{arxiv.2508.11382,
title = {On Zinbiel and Tortkara superalgebras},
author = {Sofiane Bouarroudj and Farukh Mashurov},
journal= {arXiv preprint arXiv:2508.11382},
year = {2025}
}