%A ZHAO Tiao, ZHANG Chao
%T *q*-Cartan matrices of self-injective Nakayama algebras
%0 Journal Article
%D 2020
%J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
%R 10.6040/j.issn.1671-9352.0.2020.256
%P 46-51
%V 55
%N 10
%U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_3346.shtml}
%8 2020-10-20
%X The present paper mainly proves that the *q*-Cartan matrix of any self-injective Nakayama algebra *A* is diagonalizable and the determinant of *q*-Cartan|C_{A}(q)|={(1-(q^{n})^{m})/(1-q^{n}), *if*(n,m)=1;((1-q^{［m,n］})^{(m,n)})/(1-q^{n}),*if *(n,m)≠1,where *n* is the number of simple modules, *m* is the length of the shortest paths in the homogeneous ideal *I*, and *(n,m)* is the greatest common divisor of *n* and *m, ［n,m］* is the least common multiple of *n* and *m*.