The word problem for finite-rank Artin groups

Corollary 1.3 of the parabolic-intersections manuscript: there is an algorithm that, given a finite Coxeter matrix $M$, a subset $X$ and words $u,v$, decides whether $v\in uA_Xu^{-1}$; with $X=\varnothing$ this decides the word problem for every finite-rank Artin group. The algorithm uses the framed zigzag-algebra action, shown faithful in Section 8, computed exactly over a cyclotomic field, and tests one transported projective by Gaussian elimination. No complexity bound is asserted, and the conjugacy problem is not treated.

Corollary 1.3 of the parabolic-intersections manuscript: there is an algorithm that, given a finite Coxeter matrix $M$, a subset $X$ and words $u,v$, decides whether $v\in uA_Xu^{-1}$; with $X=\varnothing$ this decides the word problem for every finite-rank Artin group. The algorithm uses the framed zigzag-algebra action, shown faithful in Section 8, computed exactly over a cyclotomic field, and tests one transported projective by Gaussian elimination. No complexity bound is asserted, and the conjugacy problem is not treated.