Some infinite-dimensional simple Lie algebras in characteristic 0 related to those of Block

✍ Scribed by Dragomir Ž. Doković; Kaiming Zhao

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 727 KB
• Volume: 127
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(96)00171-5

✦ Synopsis

Given a nontrivial torsion-free abelian group (A, +, 0), a field F of characteristic 0, and a nondegenerate bi-additive skew-symmetric map cp : A x A -+ F, we study the Lie algebra _Y(A, cp) over F with basis {ex: x E A(O)} an multiplication [ex,ey] = cp(x, y)e,+,. We show that d Y(A, 'p) is simple, determine its derivations, and show that the locally finite derivations D have the form D(eX) = p(x)eX, p E Hom(A, F). We describe all isomorphisms between two such algebras. Finally, we compute H*(Y,F).