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In this note, we adapt the procedure of the Long-Moody procedure to construct linear representations of welded braid groups. We exhibit the natural setting in this context and compute the first examples of representations we obtain thanks to this method. We take this way also the opportunity to review the few known linear representations of welded braid groups.
This article extends the works of Gonc{c}alves, Guaschi, Ocampo [GGO] and Marin [MAR2] on finite subgroups of the quotients of generalized braid groups by the derived subgroup of their pure braid group. We get explicit criteria for subgroups of the (
In a recent paper by L. A. Bokut, V. V. Chaynikov and K. P. Shum in 2007, Braid group $B_n$ is represented by Artin-Buraus relations. For such a representation, it is told that all other compositions can be checked in the same way. In this note, we support this claim and check all compositions.
Let $G$ be a finite simple group of Lie type, and let $pi_G$ be the permutation representation of $G$ associated with the action of $G$ on itself by conjugation. We prove that every irreducible representation of $G$ is a constituent of $pi_G$, unless
Let $M$ be a compact surface without boundary, and $ngeq 2$. We analyse the quotient group $B_n(M)/Gamma_2(P_n(M))$ of the surface braid group $B_{n}(M)$ by the commutator subgroup $Gamma_2(P_n(M))$ of the pure braid group $P_{n}(M)$. If $M$ is diffe
Let $G$ be a simple algebraic group of type $G_2$ over an algebraically closed field of characteristic $2$. We give an example of a finite group $Gamma$ with Sylow $2$-subgroup $Gamma_2$ and an infinite family of pairwise non-conjugate homomorphisms