Theorems · Definition · group theory
Representation.diagonal
(k : Type u_1) →
[inst : Semiring k] →
(G : Type u_2) → [inst_1 : Monoid G] → (n : ℕ) → Representation k G (MonoidAlgebra k (Fin n → G))The natural k-linear G-representation on k[Gⁿ] induced by left multiplication in G.
- Defined in
- Mathlib.RepresentationTheory.Basic
- Cited by
- 2 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Monoidstatement and proof · cited by 3,887
- MonoidAlgebrastatement · cited by 590
- Representationstatement · cited by 396
- Representation.ofMulActionproof · cited by 15
Cited by4
Results whose statement or proof uses this declaration.
- Representation.diagonalOneEquivLeftRegularstatement · cited by 2
- Representation.linearizeDiagonalEquivstatement · cited by 0
- Representation.diagonalOneEquivLeftRegular_apply_singlestatement · cited by 0
- Representation.diagonalOneEquivLeftRegular_symm_apply_singlestatement · cited by 0