Theorems · Theorem · nonassociative algebras

LieModule.traceForm_eq_zero_if_mem_lcs_of_mem_ucs

∀ (R : Type u_1) (L : Type u_3) (M : Type u_4) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [inst_6 : LieModule R L M] {x y : L}
  (k : ℕ), x ∈ ⊤.lcs L k → y ∈ LieSubmodule.ucs k ⊥ → ((LieModule.traceForm R L M) x) y = 0

The upper and lower central series of L are orthogonal w.r.t. the trace form of any Lie module M.

Defined in

Mathlib.Algebra.Lie.TraceForm

Cited by

1 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule