Classification of non-lie complex filiform Leibniz algebras for low dimensions
The thesis is concerned with the structural properties of Leibniz algebras. These algebras satisfy certain identity that was suggested by J.-L.Loday (1993). When he used the tensor product instead of external product in the definition of the n-th cochain, in order to prove the differential property...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | أطروحة |
| اللغة: | English English |
| منشور في: |
2011
|
| الموضوعات: | |
| الوصول للمادة أونلاين: | http://psasir.upm.edu.my/id/eprint/25921/1/FS%202011%2057R.pdf |
| الوسوم: |
إضافة وسم
لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!
|
| id |
my-upm-ir.25921 |
|---|---|
| record_format |
uketd_dc |
| spelling |
my-upm-ir.259212022-01-26T05:11:43Z Classification of non-lie complex filiform Leibniz algebras for low dimensions 2011-05 Said Husain, Sharifah Kartini The thesis is concerned with the structural properties of Leibniz algebras. These algebras satisfy certain identity that was suggested by J.-L.Loday (1993). When he used the tensor product instead of external product in the definition of the n-th cochain, in order to prove the differential property defined on cochains,it suffices to replace the anticommutativity and Jacobi identity by the Leibniz identity. The algebras satisfying the Leibniz identity are called Leibniz algebras. We will investigate filiform Leibniz algebras. It is known that filiform Leibniz algebras arise from two sources. The first source is a naturally graded non-Lie filiform Leibniz algebras and the other one is a naturally graded filiform Lie algebras. Here we consider the class of filiform Leibniz algebras arising from the naturally graded non-Lie filiform Leibniz algebra. In 2001, Ayupov and Omirov divided this class into two subclasses. However,isomorphism problems within these classes are yet to be investigated. The classes in dimension n over a field k are denoted by FLeibn(k) and SLeibn(k), respectively. Bekbaev and Rakhimov (2006) suggested an algebraic approach to the description of isomorphism classes of filiform Leibniz algebras in terms of algebraic invariants. The main purpose of this thesis is to apply this method and find the complete classification and invariants of low dimensional complex filiform Leibniz algebras. The main result is the complete classification of complex filiform Leibniz algebras arising from the naturally graded non-Lie filiform Leibniz algebras from dimensions 5 to 8. Lie algebras - Case studies 2011-05 Thesis http://psasir.upm.edu.my/id/eprint/25921/ http://psasir.upm.edu.my/id/eprint/25921/1/FS%202011%2057R.pdf application/pdf en public doctoral Universiti Putra Malaysia Lie algebras - Case studies Faculty of Science English |
| institution |
Universiti Putra Malaysia |
| collection |
PSAS Institutional Repository |
| language |
English English |
| topic |
Lie algebras - Case studies |
| spellingShingle |
Lie algebras - Case studies Said Husain, Sharifah Kartini Classification of non-lie complex filiform Leibniz algebras for low dimensions |
| description |
The thesis is concerned with the structural properties of Leibniz algebras. These algebras satisfy certain identity that was suggested by J.-L.Loday (1993). When he used the tensor product instead of external product in the definition of the n-th cochain, in order to prove the differential property defined on cochains,it suffices to replace the anticommutativity and Jacobi identity by the Leibniz identity. The algebras satisfying the Leibniz identity are called Leibniz algebras. We will investigate filiform Leibniz algebras. It is known that filiform Leibniz algebras arise from two sources. The first source is a naturally graded non-Lie filiform Leibniz algebras and the other one is a naturally graded filiform Lie algebras. Here we consider the class of filiform Leibniz algebras arising from the naturally graded non-Lie filiform Leibniz algebra. In 2001, Ayupov and Omirov divided this class into two subclasses. However,isomorphism problems within these classes are yet to be investigated. The classes in dimension n over a field k are denoted by FLeibn(k) and SLeibn(k), respectively. Bekbaev and Rakhimov (2006) suggested an algebraic approach to the description of isomorphism classes of filiform Leibniz algebras in terms of algebraic invariants. The main purpose of this thesis is to apply this method and find the complete classification and invariants of low dimensional complex filiform Leibniz algebras. The main result is the complete classification of complex filiform Leibniz algebras arising from the naturally graded non-Lie filiform Leibniz algebras from dimensions 5 to 8. |
| format |
Thesis |
| qualification_level |
Doctorate |
| author |
Said Husain, Sharifah Kartini |
| author_facet |
Said Husain, Sharifah Kartini |
| author_sort |
Said Husain, Sharifah Kartini |
| title |
Classification of non-lie complex filiform Leibniz algebras for low dimensions |
| title_short |
Classification of non-lie complex filiform Leibniz algebras for low dimensions |
| title_full |
Classification of non-lie complex filiform Leibniz algebras for low dimensions |
| title_fullStr |
Classification of non-lie complex filiform Leibniz algebras for low dimensions |
| title_full_unstemmed |
Classification of non-lie complex filiform Leibniz algebras for low dimensions |
| title_sort |
classification of non-lie complex filiform leibniz algebras for low dimensions |
| granting_institution |
Universiti Putra Malaysia |
| granting_department |
Faculty of Science |
| publishDate |
2011 |
| url |
http://psasir.upm.edu.my/id/eprint/25921/1/FS%202011%2057R.pdf |
| _version_ |
1747811532922683392 |