Theorems · Definition · nonassociative algebras

LieModule.lowerCentralSeriesLast

(R : Type u) →
  (L : Type v) →
    (M : Type w) →
      [inst : CommRing R] →
        [inst_1 : LieRing L] →
          [LieAlgebra R L] →
            [inst_3 : AddCommGroup M] → [inst_4 : Module R M] → [inst_5 : LieRingModule L M] → LieSubmodule R L M

Given a non-trivial nilpotent Lie module M with lower central series M = C₀ ≥ C₁ ≥ ⋯ ≥ Cₖ = ⊥, this is the k-1th term in the lower central series (the last non-trivial term). For a trivial or non-nilpotent module, this is the bottom submodule, ⊥.

Defined in

Mathlib.Algebra.Lie.Nilpotent

Cited by

4 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModule