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Zbl 0988.20021
Bigelow, Stephen J.
Braid groups are linear.
(English)
[J] J. Am. Math. Soc. 14, No. 2, 471-486 (2001). ISSN 0894-0347; ISSN 1088-6834/e

{\it D. Krammer} [Invent. Math. 142, No. 3, 451-486 (2000; see the review Zbl 0988.20023 below)] proved that a representation of the braid groups $B_n$ is faithful in the case $n=4$. The representation Krammer used is essentially the same as one used by {\it R. J. Lawrence} [Commun. Math. Phys. 135, No. 1, 141-191 (1990; Zbl 0716.20022)]. The author calls this representation the Lawrence-Krammer representation.\par In the paper the author proves by topological methods that the Lawrence-Krammer representation is faithful for all $n$.
[Andrei M.Akimenkov (Krasnogorsk)]
MSC 2000:
*20F36 Braid groups; Artin groups
20C15 Ordinary representations and characters of groups
57M07 Topological methods in group theory

Keywords: braid groups; linear groups; representations

Citations: Zbl 0988.20023; Zbl 0716.20022

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