On completeness of some pro-solvable Lie algebras

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

doi:10.2298/FIL2319395A

On completeness of some pro-solvable Lie algebras

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

Academy of Sciences of the Republic of Uzbekistan
National University of Uzbekistan named after Mirzo Ulugbek
New Uzbekistan University
Faculty of Computer and Mathematical Sciences

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

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⁾ and A⁽²⁾, respectively. Then 1 2 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.

Original language	English
Pages (from-to)	6395-6415
Number of pages	21
Journal	Filomat
Volume	37
Issue number	19
DOIs	https://doi.org/10.2298/FIL2319395A
State	Published - 2023
Externally published	Yes

Keywords

Cohomology group
Lie algebra
Potentially nilpotent Lie algebra
Pro-nilpotent (pro-solvable) Lie algebra

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10.2298/FIL2319395A

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title = "On completeness of some pro-solvable Lie algebras",

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) and A(2), respectively. Then 1 2 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.",

keywords = "Cohomology group, Lie algebra, Potentially nilpotent Lie algebra, Pro-nilpotent (pro-solvable) Lie algebra",

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

year = "2023",

doi = "10.2298/FIL2319395A",

language = "英语",

volume = "37",

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journal = "Filomat",

issn = "0354-5180",

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T1 - On completeness of some pro-solvable Lie algebras

AU - Abdurasulov, K. K.

AU - Omirov, B. A.

AU - Rakhimov, I. S.

AU - Solijanova, G. O.

PY - 2023

Y1 - 2023

N2 - 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) and A(2), respectively. Then 1 2 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.

AB - 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) and A(2), respectively. Then 1 2 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.

KW - Cohomology group

KW - Lie algebra

KW - Potentially nilpotent Lie algebra

KW - Pro-nilpotent (pro-solvable) Lie algebra

UR - https://www.scopus.com/pages/publications/85151943729

U2 - 10.2298/FIL2319395A

DO - 10.2298/FIL2319395A

M3 - 文章

AN - SCOPUS:85151943729

SN - 0354-5180

VL - 37

SP - 6395

EP - 6415

JO - Filomat

JF - Filomat

IS - 19

ER -

On completeness of some pro-solvable Lie algebras

Abstract

Keywords

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