Let g be an n-Lie superalgebra. We study the double derivation algebra 7）（g） and describe the relation between 7）（9） and the usual derivation Lie superalgebra Der（9）. We show that the set 7）（9） of all doubl...Let g be an n-Lie superalgebra. We study the double derivation algebra 7）（g） and describe the relation between 7）（9） and the usual derivation Lie superalgebra Der（9）. We show that the set 7）（9） of all double derivations is a subalgebra of the general linear Lie superalgebra gl（9） and the inner derivation algebra ad（9） is an ideal of 7）（9）. We also show that if 9 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad（9） in 7P（9） is trivial. Finally, we give that for every perfect n-Lie superalgebra 9, the triple derivations of the derivation algebra Der（9） are exactly the derivations of Der（9）.展开更多
文摘Let g be an n-Lie superalgebra. We study the double derivation algebra 7）（g） and describe the relation between 7）（9） and the usual derivation Lie superalgebra Der（9）. We show that the set 7）（9） of all double derivations is a subalgebra of the general linear Lie superalgebra gl（9） and the inner derivation algebra ad（9） is an ideal of 7）（9）. We also show that if 9 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad（9） in 7P（9） is trivial. Finally, we give that for every perfect n-Lie superalgebra 9, the triple derivations of the derivation algebra Der（9） are exactly the derivations of Der（9）.
