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McKay Matrices for Pointed Rank One Hopf Algebras of Nilpotent Type

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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 tensor-ing 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 characteris-tic polynomial and eigenvalues of Wv and give all eigenvectors of each eigenvalue for Wv when G is a dihedral group of order 4N+2.

Hopf algebraMcKay matrixgeneralized Fibonacci polynomial

Liufeng Cao、Xuejun Xia、Libin Li

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Department of Mathematics,Yangzhou University,Yangzhou,Jiangsu 225002,China

Scientific Research and Innovation Project of Graduate Students in Jiangsu ProvinceScientific Research and Innovation Project of Graduate Students in Jiangsu ProvinceNational Natural Science Foundation of China

KYCX21-3186KYCX22-344811871063

2023

10.1142/S100538672300038X

代数集刊(英文版)

代数集刊(英文版)

CSCD北大核心
ISSN：1005-3867
年,卷(期)：2023.30(3)
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