Quiver Representations

Gabriel's theorem, indecomposables, and cluster categories.


field tier

Quiver Representations. Gabriel’s theorem, indecomposables, and cluster categories.

Foundations and canonical references

The standard treatments of quiver representations approach the subject from complementary angles. Assem, Elements of the Representation Theory of Associative Algebras (2006) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Kirillov, Lectures on Quiver Varieties (2016) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.

Open methodological questions for quiver representations include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 2006
    Elements of the Representation Theory of Associative Algebras
    assem-2006, simson-2006, skowronski-2006
  • textbook · supporting · 2016
    Lectures on Quiver Varieties
    kirillov-2016

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