A quotient of the braid group related to pseudosymmetric braided categories
Abstract
Motivated by the recently introduced concept of a pseudosymmetric braided monoidal category, we define the pseudosymmetric group PSn, as the quotient of the braid group Bn by the relations σiσi+1-1σi=σ i+1σi-1σi+1, with 1≤ i≤ n-2. It turns out that PSn is isomorphic to the quotient of Bn by the commutator subgroup [Pn, Pn] of the pure braid group Pn (which amounts to saying that [Pn, Pn] coincides with the normal subgroup of Bn generated by the elements [σi2, σi+12], with 1≤ i≤ n-2), and that PSn is a linear group.
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