Examples of braided groups and braided matrices

Abstract

Matrix braided groups are developed as an analog of the ‘‘coordinate functions’’ on a group or supergroup. The ±1 in the super case is replaced by braid statistics. There are braided group analogs of all the classical simple Lie groups as well as braided matrix groups and braided matrices B(R) for every regular solution R of the quantum Yang–Baxter equations. A direct verification of B(R) is provided and some of the simplest examples are computed in detail.