JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (10): 46-51.doi: 10.6040/j.issn.1671-9352.0.2020.256

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q-Cartan matrices of self-injective Nakayama algebras

ZHAO Tiao, ZHANG Chao*   

  1. School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou, China
  • Online:2020-10-20 Published:2020-10-07

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Abstract: 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|CA(q)|={(1-(qn)m)/(1-qn), if(n,m)=1;((1-q［m,n］)(m,n))/(1-qn),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.

Key words: Cartan determinant, diagonalizable matrix, circulant matrix

CLC Number: 

  • O153.3
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