@article{Zhu2025, 
author = {Junxia Zhu and Rongsheng Ma},
title = {Generalized representations, deformations and extensions of 3-Lie superalgebras},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {22314-22335},
keywords = {3-Lie superalgebra, generalized representation, cohomology, deformation, Abelian extension, Maurer-Cartan element},
url = {https://www.sciopen.com/article/10.3934/math.2025994},
doi = {10.3934/math.2025994},
abstract = {In this paper, we introduced generalized representations of 3-Lie superalgebras, which are associated to generalized semidirect product 3-Lie superalgebras. We also developed the corresponding cohomology theory and generalized one-parameter formal deformations. Furthermore, we proved that the infinitesimals and the extensibility of finite-order deformations of generalized one-parameter formal deformations are controlled by the new first and second cohomology groups, respectively. At last, we described split and non-split Abelian extensions by generalized semidirect products and Maurer-Cartan elements, respectively.}
}