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Abstract
Heisenberg algebras are the only Lie algebras (𝔤, [,]) which verify [𝔤, 𝔤]=𝒵(𝔤 ) and dim (𝒵(𝔤 ))=1, where 𝒵 denotes the center of the algebra. We classify nilpotent Lie superalgebras that verify the same algebraic conditions in arbitrary finite dimension. We study the geometrical properties with the aid of the software Mathematica.
Acknowledgements
The authors want to thank the reviewers who provided extra references and some technical comments for our paper. The paper is Partially supported by the PAICYT, FQM143 of the Junta de Andalucía (Spain), by the Ministerio de Ciencia y Tecnología (Spain), Ref. BFM 2000-1047, and by the Junta de Extremadura-Consejería de Infraestructuras y Desarrollo Tecnológico (N. 3PR05A074).