Residually solvable extensions of an infinite dimensional filiform Leibniz algebra

2021/04/01 by Abdurasulov, K. K., Omirov, B. A., Rakhimov, I. S. +1 · 1 citation
#17B65 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2104.00557

Abstract

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.

Cited by

• Infinite dimensional analogues of nilpotent and solvable Lie algebras

Related

• Maximal solvable Leibniz algebras whose nilradical is a quasi-filiform algebra
• Solvable extensions of the naturally graded quasi-filiform Leibniz algebras
• Classification of solvable Leibniz algebras with null-filiform nilradical
• Solvable Leibniz algebras with filiform nilradical
• Solvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length