Theorems · Definition · nonassociative algebras
LieAlgebra.SpecialLinear.sl
(n : Type u_1) → (R : Type u₂) → [inst : CommRing R] → [inst_1 : DecidableEq n] → [inst_2 : Fintype n] → LieSubalgebra R (Matrix n n R)
The special linear Lie algebra: square matrices of trace zero.
- Defined in
- Mathlib.Algebra.Lie.Classical
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 84 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.
Cites8
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
- Submoduleproof · cited by 7,192
- Matrixstatement and proof · cited by 4,303
- LinearMap.kerproof · cited by 848
- LieSubalgebrastatement · cited by 418
- LieRing.ofAssociativeRingstatement · cited by 227
- Matrix.traceLinearMapproof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- LieAlgebra.SpecialLinear.singleSubSinglestatement and proof · cited by 4
- LieAlgebra.SpecialLinear.singlestatement and proof · cited by 3
- LieAlgebra.SpecialLinear.sl_bracketstatement and proof · cited by 1
- LieAlgebra.SpecialLinear.single.congr_simpstatement · cited by 0
- LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSinglestatement · cited by 0
- LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSinglestatement · cited by 0
- LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle'statement · cited by 0
- LieAlgebra.SpecialLinear.sl_non_abelianstatement and proof · cited by 0
- LieAlgebra.SpecialLinear.val_singlestatement · cited by 0
- LieAlgebra.SpecialLinear.val_singleSubSinglestatement · cited by 0