Lie superalgebras based on Heisenberg Lie algebras

Abstract

We give a complete classification of real and complex Lie superalgebras based on the Heisenberg Lie algebra ${\mathfrak{h}}_{2n+1}$. This classification generalizes previous classifications.

Keywords:

• Lie superalgebras
• adjoint representation
• symmetric equivariant maps
• Heisenberg Lie algebra

1991 Mathematics Subject Classification.:

• Primary: 17B05
• 15A21
• 17A70

Acknowledgments

The authors would like to thanks the referee for his/her comments, criticism and valuable suggestions, as they gave them the opportunity to produce a better exposition of their results by substantially improving the original presentation. The authors also acknowledge the support received by CONACyT Grant A1-S-45886 and by PRODEP Grant UASLP-CA-228.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors also acknowledge the support received by CONACyT Grant A1-S-45886 and by PRODEP Grant UASLP-CA-228.