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On tensor products of path algebras of type A

Authors
  • Hille, Lutz
  • Müller, Jürgen1, 2, 3, 4
  • 1 Mathematisches Institut
  • 2 Universität Münster
  • 3 Lehrstuhl D für Mathematik
  • 4 RWTH Aachen
Type
Published Article
Journal
Linear Algebra and its Applications
Publisher
Elsevier
Publication Date
Jan 01, 2014
Accepted Date
Jan 30, 2014
Volume
448
Pages
222–244
Identifiers
DOI: 10.1016/j.laa.2014.01.035
Source
Elsevier
Keywords
License
Unknown

Abstract

We derive a formula for the Coxeter polynomial of the s-fold tensor product ⨂i=1sF[A→ni−1] of path algebras of linearly oriented quivers of Dynkin type Ani−1, in terms of the weights n1,…,ns≥2, and show that conversely the weights can be recovered from the Coxeter polynomial of the tensor product. Our results have relevance in singularity theory, in particular these algebras occur as endomorphism algebras of tilting objects in certain stable categories of vector bundles.

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