Year: 2024
Type: article
Abstract: The objective of this research paper is to broaden the concept of Lie superalgebras into a more generalized framework known as super-Lie superalgebras. It also investigates various super-generalizations of other algebraic structures, including super-associative algebras, left (right) super-Leibniz algebras, and super-left (right)-symmetric superalgebras. The paper presents examples and fundamental results related to these structures. Additionally, it introduces the concept of Rota–Baxter operators with any parity on super-Lie superalgebras and examines representations of these superalgebras along with their associated dual representations. The study also introduces the notion of derivations of super-Lie superalgebras, demonstrating that the inverse of a bijective derivation defines a Rota–Baxter operator. Finally, it offers a generalization of super-Lie superalgebras and other related structures in the ternary case, supported by examples and interesting results.
Authors: Sami Mabrouk, Othmen Ncib
Institution: University of Gafsa
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403714435