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The Green Ring of Drinfeld Double D(H 4)

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Abstract

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.

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  1. School of Mathematical Science, Yangzhou University, Yangzhou, 225002, China

    Hui-Xiang Chen

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  1. Hui-Xiang Chen
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Correspondence to Hui-Xiang Chen.

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Chen, HX. The Green Ring of Drinfeld Double D(H 4). Algebr Represent Theor 17, 1457–1483 (2014). https://doi.org/10.1007/s10468-013-9456-5

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  • DOI: https://doi.org/10.1007/s10468-013-9456-5

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