The Green Ring of Drinfeld Double D(H 4)

In this paper, we study the Green ring (or the representation ring) of Drinfeld quantum double D(H ₄) of Sweedler’s four-dimensional Hopf algebra H ₄. We first give the decompositions of the tensor products of finite dimensional indecomposable modules into the direct sum of indecomposable modules over D(H ₄). Then we describe the structure of the Green ring r(D(H ₄)) of D(H ₄) and show that r(D(H ₄)) is generated, as a ring, by infinitely many elements subject to a family of relations.