The present paper is devoted to studying local derivations on the Lie algebra $W(2,2)$ which has some outer derivations. Using some linear algebra methods in \\cite{CZZ} and a key construction for $W(2,2)$ we p
When S is the set D(A,X) of all (bounded) derivations from a ⁎C⁎-algebra A into a Banach A-bimodule X, local D(A,X) maps are called local derivations. Local (⁎-)homomorphisms, local (⁎-)automorphisms, local Jordan (⁎-)homomorphisms and local Jordan (⁎-)...
Notice that if dim M = ∞, then not all derivations of C∞ (M) can be described as above by vector fields. Back to the finite dimension In the subsequent concluding part of this section we shall consider vector bundles of finite rank over a common base manifold M. Then, by our ...
The G-orbit of a rigid algebra should be large. For k algebraically closed, are there rigid k-algebras other than k? 3. Given the Hilbert function, are there non-trivial bounds on the dimensions of G-orbits of algebras with this Hilbert function? 4. Can the above ideas of classification...
The present paper is devoted to study 2-local derivations on W-algebra $W(2,2)$ which is an infinite-dimensional Lie algebras with some out derivations. We prove that all 2-local derivations on the W-algebra $W(2,2)$ are derivation. We also give a complete classification of the 2-...
Lie superalgebradeformative super W-algebrassuperderivation2-Local superderivation17B4017B6517B68The present article is devoted to studying 2-Local superderivations on the deformative super W -algebras (2,2). It is proved that all 2-Local superderivations on the deformative super W -algebras (...
We also characterize local and 2-local Lie derivations on some algebras such as von Neumann algebras, nest algebras, the Jiang–Su algebra, and UHF algebras.J. HeDepartment of MathematicsJ. LiDepartment of MathematicsG. AnDepartment of MathematicsW. Huang...
Local superderivations of Lie superalgebra osp(1, 2) to all simple modulesdoi:10.3934/math.20241103Shiqi ZhaoWende LiuShujuan WangAIMS Mathematics
Lie superalgebra of Block type2-local superderivationssuperderivations17B0517B4017B65In this paper, we study 2-local superderivations on the Lie superalgebra of Block type S ( q ), which is an infinite dimensional Lie superalgebra with an outer derivation. We prove that all 2-local super...
The Jacobson-Witt algebraDerivation2-local derivationRegular vectorCentralizerLIE-ALGEBRASMODULESThis paper studies local properties of Jacobson-Witt algebras over fields of prime characteristic, i.e., initiates the study on 2-local derivations of Lie algebras of prime characteristic. Let W-n be a ...