Dz. Dokovic et Km. Zhao, DERIVATIONS, ISOMORPHISMS, AND 2ND COHOMOLOGY OF GENERALIZED WITT ALGEBRAS, Transactions of the American Mathematical Society, 350(2), 1998, pp. 643-664
Generalized Witt algebras, over a field F of characteristic 0, were de
fined by Kawamoto about 12 years ago. Using different notations from K
awamoto's, we give an essentially equivalent definition of generalized
Witt algebras W = W(A, T, phi) over F, where the ingredients are an a
belian group A, a vector space T over F, and a map phi:T x A --> K whi
ch is linear in the first variable and additive in the second one. In
this paper, the derivations of any generalized Witt:algebra W = W(A, T
, phi), with the right kernel of phi being 0, are explicitly described
; the isomorphisms between any two simple generalized Witt algebras ar
e completely determined; and the second cohomology group H-2(W, F) for
any simple generalized Witt algebra is computed. The derivations, the
automorphisms and the second cohomology groups of some special genera
lized Witt algebras have been studied by several other authors as indi
cated in the references.