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• 1. Quivers and their representations: Basic definitions and examples
  • 1.1. Quivers
  • 1.2. Representations of a quiver
  • 1.3. Direct decompositions
  • 1.4. The simple representations S(x)
  • 1.5. The quivers of type A
• 2. Simple representations, thin representations.
  • 2.1. Paths
  • 2.2. (Simple representations)
  • 2.3. (Factor representations, filtrations)
  • 2.4. (Nilpotent representations)
  • 2.5. Thin representations.
• 3. Homomorphisms.
  • 3.1. Definition, some properties
  • 3.2. Endomorphism rings
  • 3.3. (Recollection of general results)
  • 3.4. Homomorphisms between thin indecomposable representations
• 4. The path algebra of a quiver
  • 4.1. Paths
  • 4.2. The path algebra of a quiver
  • 4.3. Examples of path algebras
  • 4.4. Representations of quivers, modules over the path algebra
  • 4.5. Finite dimensional k-algebras in general.
  • 4.6. The indecomposable projective kQ-modules P(x)
• 5. Extensions.
  • 5.1. Split extensions
  • 5.2. Equivalence classes of short exact sequences
  • 5.3. Construction of extensions using projective modules
  • 5.4. Realization of extensions of quivers using quiver data
  • 5.5. Modules without self-extensions.
  • 5.6. The standard guide.
  • 5.7. The standard resolution of a quiver representation.
• 6. Dynkin quivers, Euclidean quivers, wild quivers.
  • 6.1. The theorems of Gabriel and Kac.
  • 6.2. The Euler form.
  • 6.3. The quadratic form of a quiver.
  • 6.4. Dynkin quivers.
  • 6.5. More about the Dynkin quivers.
  • 6.6. Euclidean quivers.
  • 6.7. (Wild quivers).
  Correction, p 1: the number of positive roots for the type E₇ is 63 (not 69)
  • 4.7. Review of some known results from the theory of rings and modules.

The themes in brackets have not been covered.