Theorems · Theorem · nonassociative algebras

LieModule.coe_lowerCentralSeries_ideal_le

∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] {I : LieIdeal R L}
  (k : ℕ), ↑(LieModule.lowerCentralSeries R (↥I) (↥I) k) ≤ ↑(LieModule.lowerCentralSeries R L (↥I) k)

Note that the below inequality can be strict. For example the ideal of strictly-upper-triangular 2x2 matrices inside the Lie algebra of upper-triangular 2x2 matrices with k = 1.

Defined in

Mathlib.Algebra.Lie.Nilpotent

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebra