SIMPLE TWO-SIDED ANTI-LIE-ADMISSIBLE ALGEBRAS

摘要

For a Lie algebra L, a bilinear map ψ : L × L → K is called a commutative cocycle if ψ(a,b) = ψ(b,a) and ip([a, b],c) + ψ([b,a],c) + ψ([c,a],b) = 0 for any a,b,c ∈ L. We prove that any commutative cocycle of a simple Lie algebra of characteristic p ≠ 2, 3 is trivial if the rank of L is at least 2. In particular, any two-sided Alia algebra connected with a simple, finite-dimensional Lie algebra L is isomorphic to L, except for the case where L = sl_2.