Theorems · Definition · group theory
Representation.free
(k : Type u_6) →
(G : Type u_7) →
[inst : CommSemiring k] → [inst_1 : Monoid G] → (α : Type u_8) → Representation k G (α →₀ MonoidAlgebra k G)The representation on α →₀ k[G] defined pointwise by the left regular representation.
- Defined in
- Mathlib.RepresentationTheory.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- Monoidstatement and proof · cited by 3,887
- MonoidAlgebrastatement · cited by 590
- Representationstatement · cited by 396
- Representation.leftRegularproof · cited by 39
- Representation.finsuppproof · cited by 14
Cited by20
Results whose statement or proof uses this declaration.
- Rep.freeproof · cited by 9
- Representation.freeLiftstatement · cited by 5
- Rep.barComplex.d_singleproof · cited by 3
- Representation.freeLiftLEquivstatement and proof · cited by 3
- Representation.leftRegularTensorTrivialIsoFreestatement · cited by 2
- Rep.finsuppToCoinvariantsTensorFree_singlestatement and proof · cited by 1
- Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_singlestatement · cited by 1
- Representation.leftRegularTensorTrivialIsoFree_symm_apply_single_singlestatement · cited by 1
- Representation.freeAsModuleBasisstatement · cited by 1
- Representation.freeLift_single_singlestatement · cited by 1
- Representation.freeLift_toLinearMapstatement · cited by 1
- groupHomology.inhomogeneousChains.d_eqproof · cited by 0