Theorems · Definition · nonassociative algebras

LieAlgebra.zeroRootSubalgebra

(R : Type u_1) →
  (L : Type u_2) →
    [inst : CommRing R] →
      [inst_1 : LieRing L] →
        [inst_2 : LieAlgebra R L] → (H : LieSubalgebra R L) → [LieRing.IsNilpotent ↥H] → LieSubalgebra R L

Given a nilpotent Lie subalgebra H ⊆ L, the root space of the zero map 0 : H → R is a Lie subalgebra of L.

Defined in

Mathlib.Algebra.Lie.Weights.Cartan

Cited by

10 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRing.IsNilpotent