Braid Groups are Linear Groups
Copyright policy )Braid Groups are Linear Groups
Let \(B_n\) denote the braid group on \(n\) strings. \(B_2\) is infinite cyclic and hence is a linear group. It is well-known that \(B_3\) is also a linear group. But it has remained an open problem as to whether any other braid groups are linear. In 1936 Burau gave a matrix representation of \(B_n\) and in 1961 Gassner generalized Burau's representation. The author shows that \(B_n\) is linear for all \(n\) by proving Theorem A. The Gassner representation of \(B_n\) is faithful for every \(n\).
- University of California, Santa Barbara United States
- Queen Mary University of London United Kingdom
Ordinary representations and characters, Mathematics(all), braid groups, Braid groups; Artin groups, faithfulness of Gassner representations, Linear algebraic groups over arbitrary fields, free groups of finite rank, linear groups
Ordinary representations and characters, Mathematics(all), braid groups, Braid groups; Artin groups, faithfulness of Gassner representations, Linear algebraic groups over arbitrary fields, free groups of finite rank, linear groups
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