On completeness of some pro-solvable Lie algebras


K K Abdurasulov, B A Omirov, I S Rakhimov, G O Solijanova




In the paper we describe the derivations of two N-graded infinite-dimensional Lie algebras n 1 and n 2 which are the positive parts of the affine Kac-Moody algebras A (1) 1 and A (2) 2 , respectively. Then we construct all pro-solvable Lie algebras whose potential nilpotent ideals are n 1 and n 2 and compute low-dimensional (co)homology groups of the pro-solvable Lie algebras constructed.