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1 results

  • 1 - Auslander–Reiten Theory of Finite-Dimensional Algebras

  • Edited by David Jordan, University of Edinburgh, Nadia Mazza, Lancaster University, Sibylle Schroll, Universität zu Köln
  • Book:
    Modern Trends in Algebra and Representation Theory
    Published online:
    25 November 2023
    Print publication:
    17 August 2023, pp 5-45

  • Summary

    We give a brief introduction to the representation theory of finite-dimensional algebras via quivers and Auslander–Reiten theory. We describe the knitting algorithm, which gives a way to compute the Auslander–Reiten quiver of many algebras of finite-representation type. We also present recent work on the description of the representation theory of gentle and skew-gentle algebras via the geometry of oriented surfaces with boundary. An application of these geometric models is given in the context of τ-tilting theory.