SOME INFINITE-DIMENSIONAL SIMPLE LIE-ALGEBRAS IN CHARACTERISTIC-0 RELATED TO THOSE OF BLOCK

Given a nontrivial torsion-free abelian group (A,+,0), a field F of ch aracteristics 0, and a nondegenerate bi-additive skew-symmetric map ph i:AXA --> F, we study the Lie algebra L(A,phi) over F with basis {e(x) : x is an element of A\{0}} and multiplication [e(x),e(y)] = phi(x,y)E x+y. We show that L(A,phi) is simple, determine its derivations, and s how that the locally finite derivations D have the form D(e(x)) = mu(x )e(x), mu is an element of Hom(A,F). We describe all isomorphisms betw een two such algebras. Finally, we compute H-2(L,F). (C) 1998 Elsevier Science B.V. All rights reserved.