Central extension of low dimensional associative and Leibniz algebras

Leibniz algebras was introduced by Louis Loday due to several considerations in algebraic K-theory. The cyclic cohomology was somehow related to Lie algebra homology. Chevalley-Eilenberg chain complex that included in Lie algebras which the exterior powers of the Lie algebra was involved. There w...

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Main Author:	Ab Rahman, Nurnazhifa
Format:	Thesis
Language:	English
Published:	2020
Subjects:	Associative algebras Dimension theory (Algebra)
Online Access:	http://psasir.upm.edu.my/id/eprint/104715/1/NURNAZHIFA%20BINTI%20AB%20RAHMAN%20-%20IR.pdf
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spelling	my-upm-ir.1047152023-10-05T06:32:28Z Central extension of low dimensional associative and Leibniz algebras 2020-06 Ab Rahman, Nurnazhifa Leibniz algebras was introduced by Louis Loday due to several considerations in algebraic K-theory. The cyclic cohomology was somehow related to Lie algebra homology. Chevalley-Eilenberg chain complex that included in Lie algebras which the exterior powers of the Lie algebra was involved. There was a new complex which a noncommutative generalization was categorized in Lie algebra. It was called Leibniz homology as Loday is the founder. As the Lie algebra homology was related to the cyclic homology, the Leibniz homology somehow was related to the Hochschild homology. The main purpose of this thesis is to apply the Skjelbred-Sund method and find a list of isomorphism classes for associative and Leibniz algebras. The method used is to find the high dimension of algebras by using the list of low dimensional algebras. It deals with one dimensional central extension of low dimensional algebras. To get the central extension of algebras, the condition q?\C(L) = 0 need to be satisfied. If the condition is not satisfied, there is no central extension of one dimensional algebra which means this method is inapplicable. In addition, some extension invariants such as center, radical, coboundary, centroid, maximum commutative subalgebra, maximum abelian subalgebra and second cohomology are needed to investigate the isomorphism problem. As the results, seven isomorphism classes of three dimensional associative algebras, eight isomorphism classes of three dimensional Leibniz algebras and 13 isomorphism classes of four dimensional Leibniz algebra are provided. Associative algebras Dimension theory (Algebra) 2020-06 Thesis http://psasir.upm.edu.my/id/eprint/104715/ http://psasir.upm.edu.my/id/eprint/104715/1/NURNAZHIFA%20BINTI%20AB%20RAHMAN%20-%20IR.pdf text en public masters Universiti Putra Malaysia Associative algebras Dimension theory (Algebra) Said Husain, Sharifah Kartini
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
advisor	Said Husain, Sharifah Kartini
topic	Associative algebras Dimension theory (Algebra)
spellingShingle	Associative algebras Dimension theory (Algebra) Ab Rahman, Nurnazhifa Central extension of low dimensional associative and Leibniz algebras
description	Leibniz algebras was introduced by Louis Loday due to several considerations in algebraic K-theory. The cyclic cohomology was somehow related to Lie algebra homology. Chevalley-Eilenberg chain complex that included in Lie algebras which the exterior powers of the Lie algebra was involved. There was a new complex which a noncommutative generalization was categorized in Lie algebra. It was called Leibniz homology as Loday is the founder. As the Lie algebra homology was related to the cyclic homology, the Leibniz homology somehow was related to the Hochschild homology. The main purpose of this thesis is to apply the Skjelbred-Sund method and find a list of isomorphism classes for associative and Leibniz algebras. The method used is to find the high dimension of algebras by using the list of low dimensional algebras. It deals with one dimensional central extension of low dimensional algebras. To get the central extension of algebras, the condition q?\C(L) = 0 need to be satisfied. If the condition is not satisfied, there is no central extension of one dimensional algebra which means this method is inapplicable. In addition, some extension invariants such as center, radical, coboundary, centroid, maximum commutative subalgebra, maximum abelian subalgebra and second cohomology are needed to investigate the isomorphism problem. As the results, seven isomorphism classes of three dimensional associative algebras, eight isomorphism classes of three dimensional Leibniz algebras and 13 isomorphism classes of four dimensional Leibniz algebra are provided.
format	Thesis
qualification_level	Master's degree
author	Ab Rahman, Nurnazhifa
author_facet	Ab Rahman, Nurnazhifa
author_sort	Ab Rahman, Nurnazhifa
title	Central extension of low dimensional associative and Leibniz algebras
title_short	Central extension of low dimensional associative and Leibniz algebras
title_full	Central extension of low dimensional associative and Leibniz algebras
title_fullStr	Central extension of low dimensional associative and Leibniz algebras
title_full_unstemmed	Central extension of low dimensional associative and Leibniz algebras
title_sort	central extension of low dimensional associative and leibniz algebras
granting_institution	Universiti Putra Malaysia
publishDate	2020
url	http://psasir.upm.edu.my/id/eprint/104715/1/NURNAZHIFA%20BINTI%20AB%20RAHMAN%20-%20IR.pdf
_version_	1783725835259215872

Central extension of low dimensional associative and Leibniz algebras

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