Super-biderivations and linear super-commuting maps on infinite-dimensional Lie superalgebras

Abdaoui, M.

doi:10.22124/jart.2025.29499.1755

Super-biderivations and linear super-commuting maps on infinite-dimensional Lie superalgebras

Articles in Press

Document Type : Research Paper

Author

M. Abdaoui

University of Kairouan‎, ‎LR18ES45‎, ‎Mathematical Physics,‎‎ Quantum Modeling and Mechanical Design,Preparatory Institute for Engineering Studies of Kairouan‎, ‎Kairouan‎, ‎3100‎, ‎Tunisia

10.22124/jart.2025.29499.1755

Abstract

Let $\mathcal{G}_{\epsilon}$ (resp. $\mathcal{W}_{\epsilon}$) with $\epsilon=0$ or $\frac{1}{2}$ be the complete spectrum-generating superalgebra (resp. the centerless super Virasoro algebra). In this paper, the super-skewsymmetric super-biderivations on $\mathcal{G}_{\epsilon}$ and $\mathcal{W}_{\epsilon}$ are completely determined. In particular, we show that every super-skewsymmetric super-biderivation $\varphi$ (resp. $\phi$) of $\mathcal{G}_{\epsilon}$ (resp. $\mathcal{W}_{\epsilon}$) is inner. Based on the results of super-biderivations, we shall give the certain forms of all linear super-commuting maps on $\mathcal{G}_{\epsilon}$ and $\mathcal{W}_{\epsilon}$

Keywords