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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Burau representation is unitary
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by Craig C. Squier
Proc. Amer. Math. Soc. 90 (1984), 199-202
DOI: https://doi.org/10.1090/S0002-9939-1984-0727232-8

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
    E. Artin, Theorie der Zopfe, Hamburg Abh. 4 (1925), 47-72.
  • Joan S. Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies, No. 82, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. MR 0375281
  • Wilhelm Magnus, Braid groups: a survey, Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973) Lecture Notes in Math., Vol. 372, Springer, Berlin, 1974, pp. 463–487. MR 0353290
  • Wilhelm Magnus and Ada Peluso, On a theorem of V. I. Arnol′d, Comm. Pure Appl. Math. 22 (1969), 683–692. MR 264062, DOI 10.1002/cpa.3160220508
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Bibliographic Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 199-202
  • MSC: Primary 20F36
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0727232-8
  • MathSciNet review: 727232