The Green Ring of Drinfeld Double D(H4)

By Hui-xiang Chen. 2012

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In this paper, we study the Green ring (or the representation ring) of Drinfeld quantum double D(H4) of Sweedler’s four-dimensional Hopf algebra H4. We first give the decompositions of the tensor products of finite dimensional indecomposable modules into the direct sum of indecomposable modules over D(H4). Then we describe the structure of the Green ring r(D(H4)) of D(H4) and show that r(D(H4)) is generated, as a ring, by infinitely many elements subject to a family of relations.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/68bc35da98e3273b447a790a5e81dab3e550e816