Structure and Statistics of the Traid Group

Topological exchange statistics given by the traid group T_n can occur in one-dimensional particle systems with hard-core three-body interactions. The traid group, also known as the twin group or planar braid group, is a strand group, similar to the braid group, whose generators are self-inverses and obey locality. We compare the structures of low-order traid groups and braid groups by analyzing their conjugacy classes, normal subgroups, and word problems. Exchange statistics given by strand groups have possible applications in quantum computing and physical systems such as ultracold atoms in optical traps.