McKay matrix for indecomposable module of finite representation type Hopf algebra

Abstract

Let H be a Hopf algebra of finite representation type. For the grouplike elements and skew-primitive elements in H, we prove some general results about the eigenvalues and eigenvectors of the McKay matrix in the framework of Green ring. As an example, we investigate the McKay matrix WV of Taft algebra for tensoring with an indecomposable -module Furthermore, we compute the characteristic polynomial of WV in terms of a kind of generalized Fibonacci polynomial, and give some eigenvector(s) of each eigenvalue for WV by relating to the generalized Fibonacci polynomial. At last, we determine the eigenspaces of all eigenvalues.