Given a group $G$, the **braid operations** on an $n$-tuples of elements in $G$ are the maps

$$Q_i: (g_1, \ldots, g_{i-1}, g_i, g_{i+1}, \ldots, g_n) \to (g_1, \ldots g_{i-1}, g_i+1, g_{i+1}^{-1}g_ig_{i+1}, \ldots, g_n)$$

and their inverses, for $1 \leq i \leq n-1$. These operations generate an action on generating vectors of one refined passport.

Two generating vectors from the same refined passport are considered **braid equivalent** if they are in the same orbit under this action.

**Authors:**

**Knowl status:**

- Review status: beta
- Last edited by Jennifer Paulhus on 2020-07-16 18:59:13

**Referred to by:**

**History:**(expand/hide all)