About this Journal Submit a Manuscript Table of Contents 
ISRN Algebra
Volume 2012 (2012), Article ID 858959, 13 pages
doi:10.5402/2012/858959
Research Article

Another Proof of the Faithfulness of the Lawrence-Krammer Representation of the Braid Group 𝐡 πŸ‘

Mohammad N. Abdulrahim and Mariam Hariri

Department of Mathematics, Beirut Arab University, P.O. Box 11-5020, Beirut 11072809, Lebanon

Received 16 March 2012; Accepted 6 May 2012

Academic Editors: P. Koshlukov, H. Li, S. Yang, and Y. Zhou

Copyright © 2012 Mohammad N. Abdulrahim and Mariam Hariri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. S. Birman, Braids, Links, and Mapping Class Groups, vol. 82, Princeton University Press, Princeton, NJ, USA, 1974.
  2. D. Krammer, β€œThe braid group B4 is linear,” Inventiones Mathematicae, vol. 142, no. 3, pp. 451–486, 2000. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  3. S. J. Bigelow, β€œBraid groups are linear,” Journal of the American Mathematical Society, vol. 14, no. 2, pp. 471–486, 2001. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  4. D. Krammer, β€œBraid groups are linear,” Annals of Mathematics. Second Series, vol. 155, no. 1, pp. 131–156, 2002. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  5. R. D. Budney, β€œOn the image of the Lawrence-Krammer representation,” Journal of Knot Theory and its Ramifications, vol. 14, no. 6, pp. 773–789, 2005. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  6. M. N. Abdulrahim and M. Al-Tahan, β€œComplex specializations of Krammer's representation of the braid group, B3,” Journal of Mathematics and Statistics, vol. 4, no. 4, pp. 213–216, 2008. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  7. S. Albeverio and S. Rabanovich, β€œOn a class of unitary representations of the braid groups B3 and B4,” Institute for Applied Mathematics, vol. 611, 2007.
  8. E. Artin, β€œTheorie der zöpfe,” Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg, vol. 4, pp. 47–72, 1926.