Theorems · Definition · nonassociative algebras

LieModule.traceForm

(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] → [LieModule R L M] → LinearMap.BilinForm R L

A finite, free representation of a Lie algebra L induces a bilinear form on L called the trace form. See also killingForm.

Defined in

Mathlib.Algebra.Lie.TraceForm

Cited by

41 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule