On Zinbiel and Tortkara superalgebras
Sofiane Bouarroudj, Farukh Mashurov
TL;DR
This paper explores the structure of Zinbiel and Tortkara superalgebras, providing new examples, bases, and classifications, and establishing superalgebraic analogues of classical criteria, highlighting differences from the non-super case.
Contribution
It introduces a superalgebraic analogue of the Lie criterion, constructs bases for free Zinbiel superalgebras, and classifies Tortkara superalgebras of small dimensions.
Findings
Presented examples of Zinbiel superalgebras with Rota-Baxter operators
Constructed a basis for free Zinbiel superalgebras
Classified Tortkara superalgebras of dimensions 2 and 3
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.