Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields

Abstract

According to the classification by Kac, there are eight Cartan series and five exceptional Lie superalgebras in infinite-dimensional simple linearly compact Lie superalgebras of vector fields. In this paper, the Hom-Lie superalgebra structures on the five exceptional Lie superalgebras of vector fields are studied. By making use of the ℤ-grading structures and the transitivity, we prove that there is only the trivial Hom-Lie superalgebra structures on exceptional simple Lie superalgebras. This is achieved by studying the Hom-Lie superalgebra structures only on their 0-th and (−1)-th ℤ-components.

Keywords

• exceptional lie superalgebra
• hom-lie superalgebra structure
• gradation
• transitivity
• 17b40
• 17b65
• 17b66