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.
@article{bwmeta1.element.doi-10_1515_math-2017-0112,
author = {Liping Sun and Wende Liu},
title = {Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {1332-1343},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0112}
}
Liping Sun; Wende Liu. Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields. Open Mathematics, Tome 15 (2017) pp. 1332-1343. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0112/