Contact and Frobenius Lie superalgebras

Abstract

We introduce the concepts of complex finite-dimensional contact and Frobenius Lie superalgebras, including some relevant examples of this type of Lie superalgebras. We establish some basic properties satisfied by both contact and Frobenius Lie superalgebras, providing characterizations for both of them in terms of its associated structure supermatrix. Finally, if $\mathfrak{g}={\mathfrak{g}}_0\oplus {\mathfrak{g}}_1$ is a homogeneous even Frobenius Lie superalgebra satisfying $\text{dim}{\mathfrak{g}}_0\ne \text{dim}{\mathfrak{g}}_1,$ we show that such $\mathfrak{g}$ contains a contact superideal of codimension one.

Keywords:

• Contact Lie algebras
• contact Lie superalgebras
• Frobenius Lie algebras
• Frobenius Lie superalgebras

2020 Mathematics Subject Classification:

• Primary: 17B05
• 17B99
• Secondary: 53D05
• 53D10

Acknowledgments

The authors acknowledge to the referee for providing valuable comments that improved this manuscript.

Disclosure statement

There is no conflict of interest.

Additional information

Funding

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