Decomposition theory of modules: the case of Kronecker algebra

Hideto Asashiba, Ken Nakashima, Michio Yoshiwaki

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Let A be a finite-dimensional algebra over an algebraically closed field k. For any finite-dimensional A-module M we give a general formula that computes the indecomposable decomposition of M without decomposing it, for which we use the knowledge of AR-quivers that are already computed in many cases. The proof of the formula here is much simpler than that in a prior literature by Dowbor and Mróz. As an example we apply this formula to the Kronecker algebra A and give an explicit formula to compute the indecomposable decomposition of M, which enables us to make a computer program.

Original languageEnglish
Pages (from-to)489-507
Number of pages19
JournalJapan Journal of Industrial and Applied Mathematics
Issue number2
Publication statusPublished - Aug 1 2017
Externally publishedYes


  • Algebra
  • Auslander–Reiten theory
  • Decomposition
  • Kronecker algebra
  • Quiver
  • Topological data analysis

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics


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