Theorems · Theorem · group theory
Representation.ofMulAction_single
∀ {k : Type u_1} [inst : Semiring k] {G : Type u_2} [inst_1 : Monoid G] {H : Type u_3} [inst_2 : MulAction G H] (g : G)
(x : H) (r : k), ((Representation.ofMulAction k G H) g) (MonoidAlgebra.single x r) = MonoidAlgebra.single (g • x) r- Defined in
- Mathlib.RepresentationTheory.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Monoidstatement and proof · cited by 3,887
- LinearEquiv.symmproof · cited by 1,461
- MulActionstatement and proof · cited by 1,294
- Finsupp.singleproof · cited by 943
- MonoidAlgebrastatement · cited by 590
- Representationstatement · cited by 396
- MonoidAlgebra.singlestatement and proof · cited by 253
- Finsupp.lmapDomainproof · cited by 63
Cited by6
Results whose statement or proof uses this declaration.
- Rep.barComplex.d_singleproof · cited by 3
- Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_subproof · cited by 1
- Representation.leftRegular_norm_applyproof · cited by 1
- Representation.leftRegular_norm_eq_zero_iffproof · cited by 1
- Representation.FiniteCyclicGroup.coinvariantsKer_leftRegular_eq_kerproof · cited by 0
- Representation.free_single_singleproof · cited by 0