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17.16 (2010)

Open

Let $A$ be an Artin group of finite type, that is, the corresponding Coxeter group is finite. It is known that the group $A$ is linear (S. Bigelow, J. Amer. Math. Soc., 14 (2001), 471–486; D. Krammer, Ann. Math., 155 (2002), 131–156; F. Digne, J. Algebra, 268 (2003), 39–57; A. M. Cohen, D. B. Wales, Israel J. Math., 131 (2002), 101–123). Is it true that the automorphism group $\text{Aut}(A)$ is also linear?

Contributor: V. G. Bardakov

Progress

An affirmative answer for $A$ being a braid group $B_n$, $n \geqslant 2$, was obtained in (V. G. Bardakov, O. V. Bryukhanov, Vestnik Novosibirsk. Univ. Ser. Mat. Mekh. Inform., 7, no. 3 (2007), 45–58 (Russian)).

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