Theorems · Theorem · group theory
Representation.leftRegular_norm_eq_zero_iff
∀ {k : Type u_1} {G : Type u_2} [inst : CommSemiring k] [inst_1 : Group G] [inst_2 : Fintype G] (x : MonoidAlgebra k G),
(Representation.leftRegular k G).norm x = 0 ↔ (Finsupp.linearCombination k fun x => 1) x.coeff = 0- Defined in
- Mathlib.RepresentationTheory.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringGroupFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Groupstatement and proof · cited by 6,238
- Finsuppstatement · cited by 5,255
- Finset.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- Finset.univproof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- LinearMap.compproof · cited by 1,642
Cited by1
Results whose statement or proof uses this declaration.
- Representation.ker_leftRegular_norm_eqproof · cited by 1