Quiver Representations
Gabriel's theorem, indecomposables, and cluster categories.
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 · 2006Elements of the Representation Theory of Associative Algebrasassem-2006, simson-2006, skowronski-2006
- textbook · supporting · 2016Lectures on Quiver Varietieskirillov-2016
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