Theorems · Theorem · nonassociative algebras
LieAlgebra.SpecialLinear.sl_bracket
∀ (n : Type u_1) (R : Type u₂) [inst : CommRing R] [inst_1 : DecidableEq n] [inst_2 : Fintype n] (A B : ↥(LieAlgebra.SpecialLinear.sl n R)), ↑⁅A, B⁆ = ↑A * ↑B - ↑B * ↑A
- Defined in
- Mathlib.Algebra.Lie.Classical
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingDecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Bracket.bracketstatement · cited by 642
- LieSubalgebrastatement · cited by 418
- LieRing.ofAssociativeRingstatement · cited by 227
- LieAlgebra.SpecialLinear.slstatement and proof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.SpecialLinear.sl_non_abelianproof · cited by 0