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- W45468744 abstract "H → 1with the precise action of H on G suppressed. The group Hol(G) is universal in thesense that any semi-direct product G⋊H is given by the pullback obtained from ahomomorphism H → Aut(G).Recall that a group G is called linear if it admits a faithful, finite dimensionalrepresentation in Gl(m,k) for a field k of characteristic zero.The main results here addresses a special case of the following general questionstated in [4]:Question 1. Let Γ and π be linear groups. Let1 → Γ → G → π → 1be a split extension. Give conditions which imply that G is linear.It should be noted that the answer is not always positive with a basic examplegiven by Formanek and Procesi’s “poison group”([8]). Many geometrically interest-ing groups fit into the scheme given above. More specifically, examples are given bypure braid groups (and thus braid groups), McCool subgroups of Aut(F" @default.
- W45468744 created "2016-06-24" @default.
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- W45468744 date "2009-05-03" @default.
- W45468744 modified "2023-09-27" @default.
- W45468744 title "ON THE LINEARITY OF THE HOLOMORPH GROUP OF A FREE GROUP ON TWO GENERATORS" @default.
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