Theorems · Theorem · nonassociative algebras

LieAlgebra.isRegular_def

∀ (R : Type u_1) {L : Type u_3} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : Module.Finite R L] [inst_4 : Module.Free R L] (x : L),
  LieAlgebra.IsRegular R x ↔ (LinearMap.charpoly ((LieAlgebra.ad R L) x)).coeff (LieAlgebra.rank R L) ≠ 0

Defined in

Mathlib.Algebra.Lie.Rank

Cited by

0 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraModule.FiniteModule.Free