Theorems · Theorem · group theory

Representation.leftRegularTensorTrivialIsoFree_symm_apply_single_single

∀ {G : Type v} [inst : Monoid G] {k : Type u} [inst_1 : CommSemiring k] {α : Type w'} (i : α) (g : G) (r : k),
  ((Representation.leftRegularTensorTrivialIsoFree α).symm fun₀ | i => MonoidAlgebra.single g r) =
    MonoidAlgebra.single g 1 ⊗ₜ[k] MonoidAlgebra.single i r

Defined in: Mathlib.RepresentationTheory.Equiv
Cited by: 1 results in Mathlib
Foundations: Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Monoid CommSemiring

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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
CommSemiringstatement and proof · cited by 10,911
Finsuppstatement · cited by 5,255
Monoidstatement and proof · cited by 3,887
TensorProductstatement · cited by 2,545
LinearEquiv.symmproof · cited by 1,461
TensorProduct.tmulstatement and proof · cited by 1,182
Finsupp.singlestatement and proof · cited by 943
MonoidAlgebrastatement · cited by 590
LinearEquiv.transproof · cited by 298
MonoidAlgebra.singlestatement and proof · cited by 253
Representation.tprodstatement · cited by 103

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Rep.barComplex.d_comp_diagonalSuccIsoFree_inv_eqproof · cited by 0