Irreducibility of a specialization of the three dimensional Albeverio-Rabanovich representation of the pure braid group P3

Irreducibility of a specialization of the three dimensional Albeverio-Rabanovich representation of the pure braid group P3

We consider the Albeverio-Rabanovich linear representation π of the braid group B3. After specializing the indeterminates used in defining the representation to non-zero complex numbers, we prove that its restriction to the pure braid group P3 of dimension three is irreducible.

Bibliographic Details
Main Authors: Hasan A. Haidar, Mohammad N. Abdulrahim
Format: Article
Language:English
Published: Sapienza Università Editrice 2020-04-01
Series:Rendiconti di Matematica e delle Sue Applicazioni
Subjects:
braid group
pure braid group
irreducible
Online Access:https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2020(2)/155-162.pdf
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spelling doaj-c452ef650b5c477a9a09a728f9d966fc2020-12-22T14:54:10ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33502020-04-01412155162Irreducibility of a specialization of the three dimensional Albeverio-Rabanovich representation of the pure braid group P3Hasan A. Haidar0Mohammad N. Abdulrahim1Department of Mathematics and Computer Science, Beirut Arab University, P.O. Box 11-5020, Beirut, LebanonDepartment of Mathematics and Computer Science, Beirut Arab University, P.O. Box 11-5020, Beirut, LebanonWe consider the Albeverio-Rabanovich linear representation π of the braid group B3. After specializing the indeterminates used in defining the representation to non-zero complex numbers, we prove that its restriction to the pure braid group P3 of dimension three is irreducible.https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2020(2)/155-162.pdfbraid grouppure braid groupirreducible
collection DOAJ
language English
format Article
sources DOAJ
author Hasan A. Haidar
Mohammad N. Abdulrahim
spellingShingle Hasan A. Haidar
Mohammad N. Abdulrahim
Irreducibility of a specialization of the three dimensional Albeverio-Rabanovich representation of the pure braid group P3
Rendiconti di Matematica e delle Sue Applicazioni
braid group
pure braid group
irreducible
author_facet Hasan A. Haidar
Mohammad N. Abdulrahim
author_sort Hasan A. Haidar
title Irreducibility of a specialization of the three dimensional Albeverio-Rabanovich representation of the pure braid group P3
title_short Irreducibility of a specialization of the three dimensional Albeverio-Rabanovich representation of the pure braid group P3
title_full Irreducibility of a specialization of the three dimensional Albeverio-Rabanovich representation of the pure braid group P3
title_fullStr Irreducibility of a specialization of the three dimensional Albeverio-Rabanovich representation of the pure braid group P3
title_full_unstemmed Irreducibility of a specialization of the three dimensional Albeverio-Rabanovich representation of the pure braid group P3
title_sort irreducibility of a specialization of the three dimensional albeverio-rabanovich representation of the pure braid group p3
publisher Sapienza Università Editrice
series Rendiconti di Matematica e delle Sue Applicazioni
issn 1120-7183
2532-3350
publishDate 2020-04-01
description We consider the Albeverio-Rabanovich linear representation π of the braid group B3. After specializing the indeterminates used in defining the representation to non-zero complex numbers, we prove that its restriction to the pure braid group P3 of dimension three is irreducible.
topic braid group
pure braid group
irreducible
url https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2020(2)/155-162.pdf
work_keys_str_mv AT hasanahaidar irreducibilityofaspecializationofthethreedimensionalalbeveriorabanovichrepresentationofthepurebraidgroupp3
AT mohammadnabdulrahim irreducibilityofaspecializationofthethreedimensionalalbeveriorabanovichrepresentationofthepurebraidgroupp3
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