The center of the virtual braid group is trivial

Abstract

We show that the centers of the virtual braid group on n strands, VB n, and the quasitriangular group QTr n (also called the pure virtual braid group on n strands) are trivial for n ≥ 2. Furthermore, we show that the center of the triangular group Tr n (also called the pure flat braid group on n strands) is trivial for n > 2 provided Wilf's Conjecture that [Formula: see text] for n > 2 is valid, where [Formula: see text] is the nth complementary Bell number.