Representations of Algebras and Related Topics

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pp: 501–560

DOI: 10.4171/101-1/11

The minimal representation-infinite algebras which are special biserial

Claus Michael Ringel[1]

(1) Universit├Ąt Bielefeld, Germany

Let $k$ be a field. A finite dimensional k-algebra is said to be minimal representation-infinite provided it is representation-infinite and all its proper factor algebras are representation-finite. Our aim is to classify the special biserial algebras which are minimal representation-infinite. The second part describes the corresponding module categories.

Keywords: Minimal representation-infinite algebras, special biserial algebras, quiver, Auslander–Reiten quiver, Auslander–Reiten quilt, sectional paths, irreducible maps, Gorenstein algebras, semigroup algebras