Abstract

In this paper, we investigate the Green ring r(Hn,d) of the generalized Taft algebra Hn,d, extending the results of Chen, Van Oys- taeyen and Zhang in (7). We shall determine all nilpotent elements of the Green ring r(Hn,d). It turns out that each nilpotent element in r(Hn,d) can be written as a sum of indecomposable projective representations. The Jacobson radical J(r(Hn,d)) of r(Hn,d) is generated by one element, and its rank is n n/d. Moreover, we will present all the finite dimen- sional indecomposable representations over the complexified Green ring R(Hn,d) of Hn,d. Our analysis is based on the decomposition of the ten- sor product of indecomposable representations and the observation of the solutions for the system of equations associated to the generating relations of the Green ring r(Hn,d).

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