Quiver algebras and their representations (M. Barot) 
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Lecture 1: Introduction to the main notions.
Quivers, representations of quivers, isomorphic representations, morphisms
between representations, indecomposable representations. The Lemma of 
Fitting and the theorem of Krull-Remak-Schmidt.

Lecture 2: The classification problem.
Classification of all indecomposables up to isomorphisms in the linear
quiver and the loop (for this and from here on: restriction to alg. closed
ground field). A two-parameter family for the three-Kronecker quiver and the
phenomenon of wildness. Representation types.

Lecture 3: Morphisms give structure in these lists of indecomposables.
Radical morphisms form an ideal. Irreducible morphisms. The 
Auslander-Reiten quiver. The theory of Auslander-Reiten shows the 
structure of the Auslander-Reiten quiver. Very briefly: knitting. The 
theorem that a finite component is all there is. Preprojective components 
always exist.

Lecture 4: Independence of orientation.
Base changes act on representation spaces. Quadratic form and homological 
interpretation. Orbit dimensions. Gabriel's Theorem that a quiver is 
representation finite iff the associated quadratic form is positive 
definite. Very briefly: classification with Dynkin diagrams. If there is 
time: Kac's Theorem.

Lecture 5: Connection to (fin.dim.) algebras
Path algebra. Modules over path algebras. Morita equivalence. Every basic 
algebra is a quotient of a path algebra and what that means for the 
modules.