Theorems · Theorem · nonassociative algebras

RootPairing.pairing_reflectionPerm_self_left

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] (P : RootPairing ι R M N) (i j : ι),
  P.pairing ((P.reflectionPerm i) i) j = -P.pairing i j

Defined in

Mathlib.LinearAlgebra.RootSystem.Defs

Cited by

3 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule