Theorems · Definition · ring theory
skewAdjoint
(R : Type u_1) → [inst : AddCommGroup R] → [StarAddMonoid R] → AddSubgroup R
The skew-adjoint elements of a star additive group, as an additive subgroup.
- Defined in
- Mathlib.Algebra.Star.SelfAdjoint
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommGroupStarAddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- Set.ofPredproof · cited by 6,101
- AddSubgroupstatement · cited by 3,232
- Star.starproof · cited by 1,082
- StarAddMonoidstatement and proof · cited by 296
Cited by40
Results whose statement or proof uses this declaration.
- skewAdjointPartstatement · cited by 15
- skewAdjointPart_apply_coestatement · cited by 8
- IsSelfAdjoint.imaginaryPartproof · cited by 5
- skewAdjoint.negISMul_apply_coestatement and proof · cited by 5
- StarModule.decomposeProdAdjointstatement · cited by 4
- skewAdjoint.mem_iffstatement · cited by 4
- skewAdjoint.submoduleproof · cited by 4
- skewAdjoint.negISMulstatement and proof · cited by 3
- StarModule.decomposeProdAdjointLstatement and proof · cited by 2
- RCLike.I_mem_skewAdjointstatement · cited by 2
- IsSelfAdjoint.skewAdjointPart_applystatement and proof · cited by 2
- IsSelfAdjoint.smul_mem_skewAdjointstatement and proof · cited by 2