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Nilpotent elements in Green rings of a class of pointed tensor categories of finite type. (English) Zbl 1391.16018

Summary: In this paper, we will determine the nilpotent elements of the Green ring \(r(\mathcal {C})\) of a class of pointed tensor categories \(\mathcal {C}\) of finite type and the finite dimensional indecomposable representations over the complexified Green ring \(\mathbb {C}\otimes_{\mathbb {Z}} r(\mathcal {C})\).

MSC:

16N20 Jacobson radical, quasimultiplication
19A22 Frobenius induction, Burnside and representation rings
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