The Interplay between Linear Representations of the Braid Group
We consider Wada's representation as a twisted version of the standard action of the braid group, Bn, on the free group with n generators. Constructing a free group, Gnm, of rank nm, we compose Cohen's map Bn→Bnm and the embedding Bnm→Aut(Gnm) via Wada's map. We prove that the composi...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/16186 |
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| author | Mohammad N. Abdulrahim Nibal H. Kassem |
| author_facet | Mohammad N. Abdulrahim Nibal H. Kassem |
| author_sort | Mohammad N. Abdulrahim |
| collection | DOAJ |
| description | We consider Wada's representation as a twisted version of the standard action of the braid group, Bn, on the free group with n generators. Constructing a free group, Gnm, of rank nm, we compose Cohen's map Bn→Bnm and the embedding Bnm→Aut(Gnm) via Wada's map. We prove that the composition factors of the obtained
representation are one copy of Burau representation and m−1 copies of the standard representation after changing the parameter t to tk in the definitions of the Burau and standard representations. This is a generalization of our previous result concerning the standard Artin representation of the braid group. |
| format | Article |
| id | doaj-art-f5c0ceaf9dd148e192c349142f855476 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f5c0ceaf9dd148e192c349142f8554762025-02-03T01:26:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/1618616186The Interplay between Linear Representations of the Braid GroupMohammad N. Abdulrahim0Nibal H. Kassem1Department of Mathematics, Beirut Arab University, P.O. Box 11-5020, Beirut 11072809, LebanonDepartment of Mathematics, Beirut Arab University, P.O. Box 11-5020, Beirut 11072809, LebanonWe consider Wada's representation as a twisted version of the standard action of the braid group, Bn, on the free group with n generators. Constructing a free group, Gnm, of rank nm, we compose Cohen's map Bn→Bnm and the embedding Bnm→Aut(Gnm) via Wada's map. We prove that the composition factors of the obtained representation are one copy of Burau representation and m−1 copies of the standard representation after changing the parameter t to tk in the definitions of the Burau and standard representations. This is a generalization of our previous result concerning the standard Artin representation of the braid group.http://dx.doi.org/10.1155/2007/16186 |
| spellingShingle | Mohammad N. Abdulrahim Nibal H. Kassem The Interplay between Linear Representations of the Braid Group International Journal of Mathematics and Mathematical Sciences |
| title | The Interplay between Linear Representations of the Braid Group |
| title_full | The Interplay between Linear Representations of the Braid Group |
| title_fullStr | The Interplay between Linear Representations of the Braid Group |
| title_full_unstemmed | The Interplay between Linear Representations of the Braid Group |
| title_short | The Interplay between Linear Representations of the Braid Group |
| title_sort | interplay between linear representations of the braid group |
| url | http://dx.doi.org/10.1155/2007/16186 |
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