Let F be an algebraically closed field of characteristic zero, and L be a basic classical Lie superalgebra except A（n, n） over F. In this paper, we prove that every 2-local superderivation on L is a superderivation....Let F be an algebraically closed field of characteristic zero, and L be a basic classical Lie superalgebra except A（n, n） over F. In this paper, we prove that every 2-local superderivation on L is a superderivation. Furthermore, we give an example to show that a subalgebra of spl（2, 2） admits a 2-local superderivation which is not a superderivation.展开更多
By means of generators, superderivations are completely determined for a family of Lie superalgebras of special type, the tensor products of the exterior algebras and the finite-dimensional special Lie algebras over a...By means of generators, superderivations are completely determined for a family of Lie superalgebras of special type, the tensor products of the exterior algebras and the finite-dimensional special Lie algebras over a field of characteristic p〉3. In particular, the structure of the outer superderivation algebra is concretely formulated and the dimension of the first cohomology group is given.展开更多
In this paper, we prove that every local superderivation on basic classical Lie superalgebras except for A（1, 1） over the complex number field C is a superderivation. Furthermore, we give an example of a class of ni...In this paper, we prove that every local superderivation on basic classical Lie superalgebras except for A（1, 1） over the complex number field C is a superderivation. Furthermore, we give an example of a class of nilpotent Lie superalgebras with local superderivations which are not superderivations.展开更多
For an algebraically closed field F of characteristic different from 2 and a field K satisfying that for all a,b∈K,a^(2)+b^(2)=0 if and only if a=b=0,we extend the notion of superderivations to special graded local s...For an algebraically closed field F of characteristic different from 2 and a field K satisfying that for all a,b∈K,a^(2)+b^(2)=0 if and only if a=b=0,we extend the notion of superderivations to special graded local superderivations,graded local superderivations and local superderivations.Applying matrix theory,we establish a calculation method for local superderivations.Then we determine all the special graded local superderivations of Heisenberg superalgebras of even center over F and graded local superderivations and local superderivations of Heisenberg superalgebras of even center over K.Finally,we determine all the special graded local superderivations,graded local superderivations and local superderivations of Heisenberg superalgebras of odd center over F.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11471090)
文摘Let F be an algebraically closed field of characteristic zero, and L be a basic classical Lie superalgebra except A（n, n） over F. In this paper, we prove that every 2-local superderivation on L is a superderivation. Furthermore, we give an example to show that a subalgebra of spl（2, 2） admits a 2-local superderivation which is not a superderivation.
文摘By means of generators, superderivations are completely determined for a family of Lie superalgebras of special type, the tensor products of the exterior algebras and the finite-dimensional special Lie algebras over a field of characteristic p〉3. In particular, the structure of the outer superderivation algebra is concretely formulated and the dimension of the first cohomology group is given.
基金Supported by the National Natural Science Foundation of China （Grant No. 11471090）.
文摘In this paper, we prove that every local superderivation on basic classical Lie superalgebras except for A（1, 1） over the complex number field C is a superderivation. Furthermore, we give an example of a class of nilpotent Lie superalgebras with local superderivations which are not superderivations.
基金supported in part by the National Natural Science Foundation of China(12061029)Natural Science Foundation of Hainan Province(120RC587)the Natural Science Foundation of Heilongjiang Province of China(YQ2020A005).
文摘For an algebraically closed field F of characteristic different from 2 and a field K satisfying that for all a,b∈K,a^(2)+b^(2)=0 if and only if a=b=0,we extend the notion of superderivations to special graded local superderivations,graded local superderivations and local superderivations.Applying matrix theory,we establish a calculation method for local superderivations.Then we determine all the special graded local superderivations of Heisenberg superalgebras of even center over F and graded local superderivations and local superderivations of Heisenberg superalgebras of even center over K.Finally,we determine all the special graded local superderivations,graded local superderivations and local superderivations of Heisenberg superalgebras of odd center over F.
