McKay Matrices for Pointed Rank One Hopf Algebras of Nilpotent Type  

作　　者：Liufeng Cao Xuejun Xia Libin Li 

机构地区：[1]Department of Mathematics,Yangzhou University,Yangzhou,Jiangsu 225002,China

出　　处：《Algebra Colloquium》2023年第3期467-480,共14页代数集刊（英文版）

摘　　要：Let H be a finite-dimensional pointed rank one Hopf algebra of nilpotent type over a finite group G.In this paper,we investigate the McKay matrix WV of H for tensoring with the 2-dimensional indecomposable H-module V:=M(2,0).It turns out that the characteristic polynomial,eigenvalues and eigenvectors of WV are related to the character table of the finite group G and a kind of generalized Fibonacci polynomial.Moreover,we construct some eigenvectors of each eigenvalue for WV by using the factorization of the generalized Fibonacci polynomial.As an example,we explicitly compute the characteristic polynomial and eigenvalues of WV and give all eigenvectors of each eigenvalue for WV when G is a dihedral group of order 4N+2.

关 键 词：Hopf algebra McKay matrix generalized Fibonacci polynomial 

分 类 号：O15[理学—数学]