Theorems · Theorem · ring theory

AddMonoidAlgebra.antipode_single

∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : HopfAlgebra R A] {G : Type u_3}
  [inst_3 : AddGroup G] (g : G) (a : A),
  (HopfAlgebraStruct.antipode R) (AddMonoidAlgebra.single g a) =
    AddMonoidAlgebra.single (-g) ((HopfAlgebraStruct.antipode R) a)

Defined in

Mathlib.RingTheory.HopfAlgebra.MonoidAlgebra

Cited by

3 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringHopfAlgebraAddGroup