Theorems · Theorem · nonassociative algebras
LieAlgebra.IsSimple.nontrivial
∀ (R : Type u_1) (L : Type u_2) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] [LieAlgebra.IsSimple R L], Nontrivial L
A simple lie algebra is non-trivial.
- Defined in
- Mathlib.Algebra.Lie.Semisimple.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Nontrivialstatement · cited by 2,416
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- IsLieAbelianproof · cited by 55
- LieAlgebra.IsSimplestatement and proof · cited by 10
- LieAlgebra.IsSimple.non_abelianproof · cited by 2
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