JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (11): 115-121.doi: 10.6040/j.issn.1671-9352.0.2023.391

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A syzygy-infinite self-injective algebras

ZHOU Jianguo1, LIU Yuzhe1*, ZHANG Chao1, ZHANG Yafeng2   

  1. 1. School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou, China;
    2. School of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou 730020, Gansu, China
  • Published:2025-11-11

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Abstract: Let Λ be a finite dimensional k-algebra with an algebraically closed field k. It is well-known that if Λ is syzygy-finite then, by using that Λ is an n-Igusa-Todorov algebra, its finitistic dimension is finite. This paper shows that the inverse of the above proposition is false by the enveloping algebra of some Nakayama algebras, that is, there exists an algebra with finite finitistic dimension such that it is a syzygy-infinite algebra.

Key words: quiver representation, tensor algebra, enveloping algebra, finitistic dimension, self-injective dimension

CLC Number: 

  • O154
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