Theorems · Theorem · group theory
Representation.asAlgebraHom_ofMulAction_smul_eq_mul
∀ {k : Type u_1} {G : Type u_2} [inst : CommSemiring k] [inst_1 : Group G] (x y : MonoidAlgebra k G),
((Representation.ofMulAction k G G).asAlgebraHom x) y = x * y- Defined in
- Mathlib.RepresentationTheory.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- CommSemiringstatement and proof · cited by 10,911
- Groupstatement and proof · cited by 6,238
- AlgHomstatement · cited by 3,236
- one_mulproof · cited by 2,841
- one_smulproof · cited by 1,374
- map_addproof · cited by 964
- Module.Endstatement · cited by 774
- MonoidAlgebrastatement and proof · cited by 590
- map_smulproof · cited by 566
- Finsupp.extproof · cited by 399
Cited by1
Results whose statement or proof uses this declaration.
- Representation.ofMulAction_self_smul_eq_mulproof · cited by 0