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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Burau representation is unitary


Author: Craig C. Squier
Journal: Proc. Amer. Math. Soc. 90 (1984), 199-202
MSC: Primary 20F36
MathSciNet review: 727232
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Abstract: A slight modification of the Burau representation of the braid group is shown to be unitary relative to an explicitly defined Hermitian form. This gives a partial answer to the problem of identifying the image of the Burau representation and provides a tool for attacking the question of whether or not the Burau representation is faithful.


References [Enhancements On Off] (What's this?)

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  • [2] Joan S. Birman, Braids, links, and mapping class groups, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. Annals of Mathematics Studies, No. 82. MR 0375281 (51 #11477)
  • [3] Wilhelm Magnus, Braid groups: a survey, Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973) Springer, Berlin, 1974, pp. 463–487. Lecture Notes in Math., Vol. 372. MR 0353290 (50 #5774)
  • [4] Wilhelm Magnus and Ada Peluso, On a theorem of V. I. Arnol′d, Comm. Pure Appl. Math. 22 (1969), 683–692. MR 0264062 (41 #8658)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0727232-8
PII: S 0002-9939(1984)0727232-8
Article copyright: © Copyright 1984 American Mathematical Society