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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Matrix representations of Artin groups


Author: Craig C. Squier
Journal: Proc. Amer. Math. Soc. 103 (1988), 49-53
MSC: Primary 20C32; Secondary 20F36
DOI: https://doi.org/10.1090/S0002-9939-1988-0938643-3
MathSciNet review: 938643
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Abstract: We define matrix representations of Artin groups over a $ 2$-variable Laurent-polynomial ring and show that in the rank 2 case, the representations are faithful. In the special case of Artin's braid group, our representation is a version of the Burau representation and our faithfulness theorem is a generalization of the well-known fact that the Burau representation of $ {B_3}$ is faithful.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0938643-3
Article copyright: © Copyright 1988 American Mathematical Society