Abstract
This paper is devoted to studying the structures of the cell modules of the complexified Green algebra R(D(H4)), where D(H4) is the Drinfel’d quantum double of Sweedler’s 4-dimensional Hopf algebra H4. We show that R(D(H4)) has one infinite dimensional cell module, one 4-dimensional cell module generated by all finite dimensional indecomposable projective modules of D(H4) and infinitely many 2-dimensional cell modules. More precisely, we obtain the decompositions of all finite dimensional cell modules into the direct sum of indecomposable submodules, and show that the infinite dimensional cell module can be written as the direct sum of two infinite dimensional indecomposable submodules.
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Acknowledgements
The authors are grateful to V. Mazorchuk for sending us the references [6, 7, 9]. The second author was supported by National Natural Science Foundation of China (Grant No. 12071412). The third author was supported by National Natural Science Foundation of China (Grant No. 11871063). We also thank the referees for their time and comments.
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Supported by Natural National Science Foundation of China (Grant Nos. 12071412, 11871063)
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Cao, L.F., Chen, H.X. & Li, L.B. The Cell Modules of the Green Algebra of Drinfel’d Quantum Double D(H4). Acta. Math. Sin.-English Ser. 38, 1116–1132 (2022). https://doi.org/10.1007/s10114-022-9046-8
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DOI: https://doi.org/10.1007/s10114-022-9046-8