Theorems · Definition · nonassociative algebras
LieAlgebra.SpecialLinear.singleSubSingle
{n : Type u_1} →
{R : Type u₂} →
[inst : CommRing R] →
[inst_1 : DecidableEq n] → [inst_2 : Fintype n] → n → n → R →ₗ[R] ↥(LieAlgebra.SpecialLinear.sl n R)The matrices with matching positive and negative elements on the diagonal are elements of
sl n R. Along with single, a subset of these form a basis for sl n R.
- Defined in
- Mathlib.Algebra.Lie.Classical
- Cited by
- 4 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- LieSubalgebrastatement · cited by 418
- LieRing.ofAssociativeRingstatement · cited by 227
- LieSubalgebra.toSubmoduleproof · cited by 90
- LinearMap.codRestrictproof · cited by 61
- LieAlgebra.SpecialLinear.slstatement and proof · cited by 8
- Matrix.singleLinearMapproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- 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.val_singleSubSinglestatement · cited by 0