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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| Format: | Thesis |
| Language: | English |
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2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/104715/ http://psasir.upm.edu.my/id/eprint/104715/1/NURNAZHIFA%20BINTI%20AB%20RAHMAN%20-%20IR.pdf |
| _version_ | 1848864359366787072 |
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| author | Ab Rahman, Nurnazhifa |
| author_facet | Ab Rahman, Nurnazhifa |
| author_sort | Ab Rahman, Nurnazhifa |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T13:47:34Z |
| format | Thesis |
| id | upm-104715 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T13:47:34Z |
| publishDate | 2020 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1047152023-10-05T06:32:28Z http://psasir.upm.edu.my/id/eprint/104715/ Central extension of low dimensional associative and Leibniz algebras 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. 2020-06 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/104715/1/NURNAZHIFA%20BINTI%20AB%20RAHMAN%20-%20IR.pdf Ab Rahman, Nurnazhifa (2020) Central extension of low dimensional associative and Leibniz algebras. Masters thesis, Universiti Putra Malaysia. Associative algebras Dimension theory (Algebra) |
| spellingShingle | Associative algebras Dimension theory (Algebra) Ab Rahman, Nurnazhifa Central extension of low dimensional associative and Leibniz algebras |
| title | 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_short | Central extension of low dimensional associative and Leibniz algebras |
| title_sort | central extension of low dimensional associative and leibniz algebras |
| topic | Associative algebras Dimension theory (Algebra) |
| url | http://psasir.upm.edu.my/id/eprint/104715/ http://psasir.upm.edu.my/id/eprint/104715/1/NURNAZHIFA%20BINTI%20AB%20RAHMAN%20-%20IR.pdf |