Theorems · Theorem · group theory
Representation.inv_self_apply
∀ {k : Type u_1} {G : Type u_2} {V : Type u_3} [inst : Semiring k] [inst_1 : Group G] [inst_2 : AddCommMonoid V]
[inst_3 : Module k V] (ρ : Representation k G V) (g : G) (x : V), (ρ g⁻¹) ((ρ g) x) = x- Defined in
- Mathlib.RepresentationTheory.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- Groupstatement and proof · cited by 6,238
- map_oneproof · cited by 861
- Representationstatement and proof · cited by 396
- inv_mul_cancelproof · cited by 107
Cited by12
Results whose statement or proof uses this declaration.
- Representation.apply_bijectiveproof · cited by 3
- groupHomology.d₂₁_single_ρ_add_single_inv_mulproof · cited by 1
- groupHomology.d₂₁_single_self_inv_ρ_sub_inv_selfproof · cited by 0
- groupHomology.single_mem_cycles₂_iffproof · cited by 0
- Representation.Coinvariants.mk_inv_tmulproof · cited by 0
- groupHomology.single_one_snd_sub_single_one_fst_mem_boundaries₂proof · cited by 0
- Representation.Coinvariants.mk_tmul_invproof · cited by 0
- Representation.inv_apply_eq_iffproof · cited by 0
- groupHomology.d₁₀_single_invproof · cited by 0
- Representation.mem_invariants_iff_of_forall_mem_zpowersproof · cited by 0
- Representation.Coinvariants.le_comap_kerproof · cited by 0
- Representation.mem_linHom_invariants_iff_isIntertwiningproof · cited by 0