The Burau representation is unitary
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- by Craig C. Squier PDF
- Proc. Amer. Math. Soc. 90 (1984), 199-202 Request permission
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
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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
Additional 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