On Zinbiel and Tortkara superalgebras

Fuente: arXiv
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Main Authors: Bouarroudj, Sofiane, Mashurov, Farukh
Format: Preprint
Published: 2025
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author Bouarroudj, Sofiane
Mashurov, Farukh
author_facet Bouarroudj, Sofiane
Mashurov, Farukh
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_11382
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On Zinbiel and Tortkara superalgebras
Bouarroudj, Sofiane
Mashurov, Farukh
Rings and Algebras
17A30, 17A50, 17A70
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.
title On Zinbiel and Tortkara superalgebras
topic Rings and Algebras
17A30, 17A50, 17A70
url https://arxiv.org/abs/2508.11382