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

Liping Sun, and Wende Liu. "Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields." Open Mathematics 15.1 (2017): 1332-1343. <http://eudml.org/doc/288434>.

@article{LipingSun2017,
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.},
author = {Liping Sun, Wende Liu},
journal = {Open Mathematics},
keywords = {Exceptional Lie superalgebra; Hom-Lie superalgebra structure; Gradation; Transitivity},
language = {eng},
number = {1},
pages = {1332-1343},
title = {Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields},
url = {http://eudml.org/doc/288434},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Liping Sun
AU - Wende Liu
TI - Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 1332
EP - 1343
AB - 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.
LA - eng
KW - Exceptional Lie superalgebra; Hom-Lie superalgebra structure; Gradation; Transitivity
UR - http://eudml.org/doc/288434
ER -