On completeness of some pro-solvable Lie algebras
Kobiljon AbdurasulovV.I.Romanovski Institute of Mathematics Uzbekistan Academy of Sciences, Tashkent, UzbekistanB. A. OmirovNational University of Uzbekistan, Tashkent, Uzbekistan + New Uzbekistan University, Tashkent, Uzbekistan + V.I. Romanovski Institute of Mathematics Uzbekistan Academy of Sciences, Tashkent, UzbekistanI. S. RakhimovFaculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM), Shah Alam, Selangor Darul Ehsan, MalaysiaG.O. SolijanovabNational University of Uzbekistan, Tashkent, Uzbekistan
ABI
Abstract
In the paper we describe the derivations of two N-graded infinite-dimensional Lie algebras n1 and n2 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 n1 and n2 and compute low-dimensional (co)homology groups of the pro-solvable Lie algebras constructed.
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