Classification and derivations of low-dimensional complex dialgebras

The thesis is mainly comprised of two parts. In the first part we consider the classification problem of low-dimensional associative, diassociative and dendriform algebras. Since so far there are no research results dealing with representing diassociative and dendriform algebras in form of precis...

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Main Author:	Basri, Witriany
Format:	Thesis
Language:	English
Published:	2014
Subjects:	Algebra Lie algebras Low-dimensional topology
Online Access:	http://psasir.upm.edu.my/id/eprint/70472/1/FS%202014%2047%20-%20IR.pdf
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spelling	my-upm-ir.704722019-10-30T03:46:52Z Classification and derivations of low-dimensional complex dialgebras 2014-12 Basri, Witriany The thesis is mainly comprised of two parts. In the first part we consider the classification problem of low-dimensional associative, diassociative and dendriform algebras. Since so far there are no research results dealing with representing diassociative and dendriform algebras in form of precise tables under some basis, it is desirable to have such lists up to isomorphisms. There is no standard approach to the classification problem of algebras. One of the approaches which can be applied is to fix a basis and represent the algebras in terms of structure constants. Due to the identities we have constraints for the structure constants in polynomial form. Solving the system of polynomials we get a redundant list of all the algebras from given class. Then we erase isomorphic copies from the list. It is slightly tedious to perform this procedure by hand. For this case we construct and use several computer programs. They are applied to verify the isomorphism between found algebras, to find automorphism groups and verify the algebra identities. In conclusion, we give complete lists of isomorphism classes for diassociative and dendriform algebras in low dimensions. We found for diassociative algebras four isomorphism classes (one parametric family and another three are single class) in dimension two, 17 isomorphism classes (one parametric family and others are single classes) in dimension three and for nilpotent diassociative algebras we obtain 16 isomorphism classes (all of them are parametric family) in dimension four. In dendriform algebras case there are twelve isomorphism classes (one parametric family and another eleven are single classes) in dimension two. The second part of the thesis is devoted to the computation of derivations of low-dimensional associative, diassociative and dendriform algebras. We give the derivations the above mentioned classes of algebras in dimensions two and three. Algebra Lie algebras Low-dimensional topology 2014-12 Thesis http://psasir.upm.edu.my/id/eprint/70472/ http://psasir.upm.edu.my/id/eprint/70472/1/FS%202014%2047%20-%20IR.pdf text en public doctoral Universiti Putra Malaysia Algebra Lie algebras Low-dimensional topology
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Algebra Lie algebras Low-dimensional topology
spellingShingle	Algebra Lie algebras Low-dimensional topology Basri, Witriany Classification and derivations of low-dimensional complex dialgebras
description	The thesis is mainly comprised of two parts. In the first part we consider the classification problem of low-dimensional associative, diassociative and dendriform algebras. Since so far there are no research results dealing with representing diassociative and dendriform algebras in form of precise tables under some basis, it is desirable to have such lists up to isomorphisms. There is no standard approach to the classification problem of algebras. One of the approaches which can be applied is to fix a basis and represent the algebras in terms of structure constants. Due to the identities we have constraints for the structure constants in polynomial form. Solving the system of polynomials we get a redundant list of all the algebras from given class. Then we erase isomorphic copies from the list. It is slightly tedious to perform this procedure by hand. For this case we construct and use several computer programs. They are applied to verify the isomorphism between found algebras, to find automorphism groups and verify the algebra identities. In conclusion, we give complete lists of isomorphism classes for diassociative and dendriform algebras in low dimensions. We found for diassociative algebras four isomorphism classes (one parametric family and another three are single class) in dimension two, 17 isomorphism classes (one parametric family and others are single classes) in dimension three and for nilpotent diassociative algebras we obtain 16 isomorphism classes (all of them are parametric family) in dimension four. In dendriform algebras case there are twelve isomorphism classes (one parametric family and another eleven are single classes) in dimension two. The second part of the thesis is devoted to the computation of derivations of low-dimensional associative, diassociative and dendriform algebras. We give the derivations the above mentioned classes of algebras in dimensions two and three.
format	Thesis
qualification_level	Doctorate
author	Basri, Witriany
author_facet	Basri, Witriany
author_sort	Basri, Witriany
title	Classification and derivations of low-dimensional complex dialgebras
title_short	Classification and derivations of low-dimensional complex dialgebras
title_full	Classification and derivations of low-dimensional complex dialgebras
title_fullStr	Classification and derivations of low-dimensional complex dialgebras
title_full_unstemmed	Classification and derivations of low-dimensional complex dialgebras
title_sort	classification and derivations of low-dimensional complex dialgebras
granting_institution	Universiti Putra Malaysia
publishDate	2014
url	http://psasir.upm.edu.my/id/eprint/70472/1/FS%202014%2047%20-%20IR.pdf
_version_	1747812845953744896

Classification and derivations of low-dimensional complex dialgebras

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