THE GREEN RINGS OF THE GENERALIZED TAFT HOPF ALGEBRAS

By Libin Li, Yinhuo Zhang. 2012

56 citations recorded by the source corpus.

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).

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6598d1829733c5b013263bdfcb57f45f750d51ab

Citations in the corpus

• The Green Ring of Drinfeld Double D(H4) (2012, unknown): “Recently, Chen, Van Oystaeyen and Zhang computed the Green rings of Taft algebras Hn(q) in [11], Li and Zhang studied the Green rings of the generalized Taft algebras in [18].”