Theorems · Theorem · nonassociative algebras
LieDerivation.toLinearMapLieHom_injective
∀ (R : Type u_1) (L : Type u_2) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L], Function.Injective ⇑(LieDerivation.toLinearMapLieHom R L)
The map from Lie derivations to linear endomorphisms is injective.
- Defined in
- Mathlib.Algebra.Lie.Derivation.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
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Cites11
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieHomstatement · cited by 382
- LieRing.ofAssociativeRingstatement · cited by 227
- LieDerivationstatement and proof · cited by 95
- LieDerivation.extproof · cited by 7
- LieDerivation.toLinearMapLieHomstatement and proof · cited by 1
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