On Zinbiel and Tortkara Superalgebras
Bouarroudj S. Mashurov F.
September 2025Springer Science and Business Media Deutschland GmbH
Bulletin of the Brazilian Mathematical Society
2025#56Issue 3
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.
Algebraic classification , Lie element , Tortkara superalgebra , Zinbiel superalgebra
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Division of Science and Mathematics, New York University Abu Dhabi, Abu Dhabi, 129188, United Arab Emirates
SDU University, Kaskelen, Kazakhstan
Shenzhen International Center for Mathematics, Shenzhen, 518055, China
Division of Science and Mathematics
SDU University
Shenzhen International Center for Mathematics
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