Theorems · Theorem · group theory

CoxeterSystem.wordProd_braidWord_eq

∀ {B : Type u_1} {W : Type u_3} [inst : Group W] {M : CoxeterMatrix B} (cs : CoxeterSystem M W) (i i' : B),
  cs.wordProd (CoxeterSystem.braidWord M i i') = cs.wordProd (CoxeterSystem.braidWord M i' i)

The two words of length M i i' that alternate between i and i' have the same product. This is known as the "braid relation" or "Artin-Tits relation".

Defined in

Mathlib.GroupTheory.Coxeter.Basic

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Group