Weak Hopf Algebra and Its Quiver Representation

This study induced a weak Hopf algebra from the path coalgebra of a weak Hopf quiver. Moreover, it gave a quiver representation of the said algebra which gives rise to the various structures of the so-called weak Hopf algebra through the quiver. Furthermore, it also showed the canonical representati...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Muhammad Naseer Khan, Ahmed Munir, Muhammad Arshad, Ahmed Alsanad, Suheer Al-Hadhrami
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/4604f2d9068342aca2317c230da02376
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:4604f2d9068342aca2317c230da02376
record_format	dspace
spelling	oai:doaj.org-article:4604f2d9068342aca2317c230da023762021-11-15T01:20:11ZWeak Hopf Algebra and Its Quiver Representation1563-514710.1155/2021/1483371https://doaj.org/article/4604f2d9068342aca2317c230da023762021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/1483371https://doaj.org/toc/1563-5147This study induced a weak Hopf algebra from the path coalgebra of a weak Hopf quiver. Moreover, it gave a quiver representation of the said algebra which gives rise to the various structures of the so-called weak Hopf algebra through the quiver. Furthermore, it also showed the canonical representation for each weak Hopf quiver. It was further observed that a Cayley digraph of a Clifford monoid can be embedded in its corresponding weak Hopf quiver of a Clifford monoid. This lead to the development of the foundation structures of weak Hopf algebra. Such quiver representation is useful for the classification of its path coalgebra. Additionally, some structures of module theory of algebra were also given. Such algebras can also be applied for obtaining the solutions of “quantum Yang–Baxter equation” that has many applications in the dynamical systems for finding interesting results.Muhammad Naseer KhanAhmed MunirMuhammad ArshadAhmed AlsanadSuheer Al-HadhramiHindawi LimitedarticleEngineering (General). Civil engineering (General)TA1-2040MathematicsQA1-939ENMathematical Problems in Engineering, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
spellingShingle	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939 Muhammad Naseer Khan Ahmed Munir Muhammad Arshad Ahmed Alsanad Suheer Al-Hadhrami Weak Hopf Algebra and Its Quiver Representation
description	This study induced a weak Hopf algebra from the path coalgebra of a weak Hopf quiver. Moreover, it gave a quiver representation of the said algebra which gives rise to the various structures of the so-called weak Hopf algebra through the quiver. Furthermore, it also showed the canonical representation for each weak Hopf quiver. It was further observed that a Cayley digraph of a Clifford monoid can be embedded in its corresponding weak Hopf quiver of a Clifford monoid. This lead to the development of the foundation structures of weak Hopf algebra. Such quiver representation is useful for the classification of its path coalgebra. Additionally, some structures of module theory of algebra were also given. Such algebras can also be applied for obtaining the solutions of “quantum Yang–Baxter equation” that has many applications in the dynamical systems for finding interesting results.
format	article
author	Muhammad Naseer Khan Ahmed Munir Muhammad Arshad Ahmed Alsanad Suheer Al-Hadhrami
author_facet	Muhammad Naseer Khan Ahmed Munir Muhammad Arshad Ahmed Alsanad Suheer Al-Hadhrami
author_sort	Muhammad Naseer Khan
title	Weak Hopf Algebra and Its Quiver Representation
title_short	Weak Hopf Algebra and Its Quiver Representation
title_full	Weak Hopf Algebra and Its Quiver Representation
title_fullStr	Weak Hopf Algebra and Its Quiver Representation
title_full_unstemmed	Weak Hopf Algebra and Its Quiver Representation
title_sort	weak hopf algebra and its quiver representation
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/4604f2d9068342aca2317c230da02376
work_keys_str_mv	AT muhammadnaseerkhan weakhopfalgebraanditsquiverrepresentation AT ahmedmunir weakhopfalgebraanditsquiverrepresentation AT muhammadarshad weakhopfalgebraanditsquiverrepresentation AT ahmedalsanad weakhopfalgebraanditsquiverrepresentation AT suheeralhadhrami weakhopfalgebraanditsquiverrepresentation
_version_	1718428918508158976

Weak Hopf Algebra and Its Quiver Representation

Ejemplares similares