Residually solvable extensions of an infinite dimensional filiform Leibniz algebra

K. K. Abdurasulov; B. A. Omirov; I. S. Rakhimov; G. O. Solijanova

doi:10.1016/j.jalgebra.2021.06.024

Residually solvable extensions of an infinite dimensional filiform Leibniz algebra

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

^*Corresponding author for this work

Academy of Sciences of the Republic of Uzbekistan
National University of Uzbekistan named after Mirzo Ulugbek
Universiti Teknologi MARA

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In the paper we describe the class of all solvable extensions of an infinite-dimensional filiform Leibniz algebra. The filiform Leibniz algebra is taken as a maximal pro-nilpotent ideal of a residually solvable Leibniz algebra. It is proven that the second cohomology group of the extension is trivial.

Original language	English
Pages (from-to)	697-722
Number of pages	26
Journal	Journal of Algebra
Volume	585
DOIs	https://doi.org/10.1016/j.jalgebra.2021.06.024
State	Published - 1 Nov 2021
Externally published	Yes

Keywords

Cohomology group
Lie algebra
Potentially nilpotent Lie algebra
Pro-nilpotent Lie algebra

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10.1016/j.jalgebra.2021.06.024

Cite this

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title = "Residually solvable extensions of an infinite dimensional filiform Leibniz algebra",

abstract = "In the paper we describe the class of all solvable extensions of an infinite-dimensional filiform Leibniz algebra. The filiform Leibniz algebra is taken as a maximal pro-nilpotent ideal of a residually solvable Leibniz algebra. It is proven that the second cohomology group of the extension is trivial.",

keywords = "Cohomology group, Lie algebra, Potentially nilpotent Lie algebra, Pro-nilpotent Lie algebra",

author = "Abdurasulov, \{K. K.\} and Omirov, \{B. A.\} and Rakhimov, \{I. S.\} and Solijanova, \{G. O.\}",

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AU - Solijanova, G. O.

PY - 2021/11/1

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N2 - In the paper we describe the class of all solvable extensions of an infinite-dimensional filiform Leibniz algebra. The filiform Leibniz algebra is taken as a maximal pro-nilpotent ideal of a residually solvable Leibniz algebra. It is proven that the second cohomology group of the extension is trivial.

AB - In the paper we describe the class of all solvable extensions of an infinite-dimensional filiform Leibniz algebra. The filiform Leibniz algebra is taken as a maximal pro-nilpotent ideal of a residually solvable Leibniz algebra. It is proven that the second cohomology group of the extension is trivial.

KW - Cohomology group

KW - Lie algebra

KW - Potentially nilpotent Lie algebra

KW - Pro-nilpotent Lie algebra

UR - https://www.scopus.com/pages/publications/85114753629

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ER -

Residually solvable extensions of an infinite dimensional filiform Leibniz algebra

Abstract

Keywords

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