Theorems · Definition · nonassociative algebras

LieSubmodule.IsUcsLimit

{R : Type u} →
  {L : Type v} →
    [inst : CommRing R] →
      [inst_1 : LieRing L] →
        [inst_2 : LieAlgebra R L] →
          {M : Type u_1} →
            [inst_3 : AddCommGroup M] →
              [inst_4 : Module R M] → [inst_5 : LieRingModule L M] → [LieModule R L M] → LieSubmodule R L M → Prop

Given a Lie module M of a Lie algebra L, LieSubmodule.IsUcsLimit is the proposition that a Lie submodule N ⊆ M is the limiting value for the upper central series. This is a characteristic property of Cartan subalgebras with the roles of L, M, N played by H, L, H, respectively. See LieSubalgebra.isCartanSubalgebra_iff_isUcsLimit.

Defined in

Mathlib.Algebra.Lie.CartanSubalgebra

Cited by

1 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule