The minimal number of generators for finite-dimensional Cartan Lie superalgebras
Volume 158 / 2019
Colloquium Mathematicum 158 (2019), 305-312 MSC: Primary 17B05; Secondary 17B20. DOI: 10.4064/cm7628-11-2018 Published online: 5 September 2019
Suppose the ground field is algebraically closed and of characteristic zero. We prove that any finite-dimensional Cartan Lie superalgebra is generated by one element. Combined with a result due to Albuquerque and Elduque for classical Lie superalgebras, this implies that any finite-dimensional Lie superalgebra is generated by one element.