Generalizations of the standard Artin representation are unitary
We consider the Magnus representation of the image of the braid group under the generalizations of the standard Artin representation discovered by M. Wada. We show that the images of the generators of the braid group under the Magnus representation are unitary relative to a Hermitian matrix. As a...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1321 |
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| _version_ | 1832549213290889216 |
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| author | Mohammad N. Abdulrahim |
| author_facet | Mohammad N. Abdulrahim |
| author_sort | Mohammad N. Abdulrahim |
| collection | DOAJ |
| description | We consider the Magnus representation of the image of the braid group under the generalizations of the standard Artin representation discovered by M. Wada. We show that the images of the generators of the braid group under the Magnus representation are unitary relative to a Hermitian matrix. As a special case,
we get that the Burau representation is unitary, which was known and proved by C. C. Squier. |
| format | Article |
| id | doaj-art-0d13f3f7b8e14699aaaff716d9d7bdeb |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0d13f3f7b8e14699aaaff716d9d7bdeb2025-02-03T06:11:44ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-01200581321132610.1155/IJMMS.2005.1321Generalizations of the standard Artin representation are unitaryMohammad N. Abdulrahim0Department of Mathematics, Faculty of Science, Beirut Arab University, P.O. Box 11-5020, Beirut 1107 2809, LebanonWe consider the Magnus representation of the image of the braid group under the generalizations of the standard Artin representation discovered by M. Wada. We show that the images of the generators of the braid group under the Magnus representation are unitary relative to a Hermitian matrix. As a special case, we get that the Burau representation is unitary, which was known and proved by C. C. Squier.http://dx.doi.org/10.1155/IJMMS.2005.1321 |
| spellingShingle | Mohammad N. Abdulrahim Generalizations of the standard Artin representation are unitary International Journal of Mathematics and Mathematical Sciences |
| title | Generalizations of the standard Artin representation are unitary |
| title_full | Generalizations of the standard Artin representation are unitary |
| title_fullStr | Generalizations of the standard Artin representation are unitary |
| title_full_unstemmed | Generalizations of the standard Artin representation are unitary |
| title_short | Generalizations of the standard Artin representation are unitary |
| title_sort | generalizations of the standard artin representation are unitary |
| url | http://dx.doi.org/10.1155/IJMMS.2005.1321 |
| work_keys_str_mv | AT mohammadnabdulrahim generalizationsofthestandardartinrepresentationareunitary |