Residually solvable extensions of an infinite dimensional filiform Leibniz algebra
Kobiljon AbdurasulovNational University of Uzbekistan, Tashkent, UzbekistanB. A. OmirovNational University of Uzbekistan, Tashkent, UzbekistanI. S. RakhimovNational University of Uzbekistan, Tashkent, UzbekistanG.O. SolijanovaNational University of Uzbekistan, TAshkent, Uzbekistan
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In the paper the class of all solvable extensions of a filiform Leibniz algebra in the infinite-dimensional case is classified. The filiform Leibniz algebra is taken as a maximal pro-nilpotent ideal of residually solvable Leibniz algebra. It is proven that the second cohomology group of the extension is trivial.
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