Theorems · Theorem · nonassociative algebras

RootPairing.GeckConstruction.cartanSubalgebra_eq_lieSpan

∀ {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}
  [inst_5 : P.IsCrystallographic] (b : P.Base) [inst_6 : Fintype ι] [inst_7 : DecidableEq ι],
  RootPairing.GeckConstruction.cartanSubalgebra b =
    LieSubalgebra.lieSpan R (Matrix (↥b.support ⊕ ι) (↥b.support ⊕ ι) R) (Set.range RootPairing.GeckConstruction.h)

Defined in

Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic

Cited by

0 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleRootPairing.IsCrystallographicFintypeDecidableEq