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Zbl 0988.20023
Krammer, Daan
The braid group $B_4$ is linear. (English)
[J] Invent. Math. 142, No. 3, 451-486 (2000). ISSN 0020-9910; ISSN 1432-1297/e

The author studies a linear representation $\rho\colon B_n\to\text{GL}_m(\bbfZ[q^{\pm 1},t^{\pm 1}])$ (where $m=n(n-1)/2$). Instead of the usual Artin presentation of $B_n$, the author uses a new presentation with a new generating subset $Q$ and formulates a relation for the Charney length function with respect to $Q$. He formulates a conjecture implying that: (a) $\rho$ is faithful, (b) the Charney length function with respect to $Q$ satisfies the relation. The author proves this conjecture for $n=4$.
[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 representations; Artin presentations; Charney length functions

Cited in: Zbl 1247.20045 Zbl 1208.20041 Zbl 1139.20032 Zbl 1020.20025 Zbl 0988.20021 Zbl 0977.57014

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