Theorems · Theorem · nonassociative algebras

LieAlgebra.finrank_engel

∀ (K : Type u_7) {L : Type u_8} [inst : Field K] [inst_1 : LieRing L] [inst_2 : LieAlgebra K L]
  [inst_3 : Module.Finite K L] (x : L),
  Module.finrank K ↥(LieSubalgebra.engel K x) = (LinearMap.charpoly ((LieAlgebra.ad K L) x)).natTrailingDegree

Defined in: Mathlib.Algebra.Lie.Rank
Cited by: 2 results in Mathlib
Foundations: Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field LieRing LieAlgebra Module.Finite

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Fieldstatement and proof · cited by 7,404
Module.finrankstatement · cited by 1,770
LieRingstatement and proof · cited by 1,548
LieAlgebrastatement and proof · cited by 1,246
Module.Finitestatement and proof · cited by 1,032
Module.Endstatement · cited by 774
LieSubalgebrastatement · cited by 418
LieHomstatement · cited by 382
LieRing.ofAssociativeRingstatement · cited by 227
Polynomial.natTrailingDegreestatement · cited by 87
LinearMap.charpolystatement · cited by 67

Cited by2

Results whose statement or proof uses this declaration.

LieAlgebra.rank_le_finrank_engelproof · cited by 1
LieAlgebra.isRegular_iff_finrank_engel_eq_rankproof · cited by 1