Teresa Conde "The Gabriel-Roiter measure revisited"

The first Brauer-Thrall conjecture, proved by Roiter in 1968, asserts that finite-dimensional algebras of bounded representation type have finite representation type. The induction scheme used in Roiter's proof prompted Gabriel to introduce an invariant, now known as the Gabriel-Roiter measure. The Gabriel-Roiter measure is a strikingly useful tool and its applicability is not limited to the first Brauer-Thrall conjecture: Ringel has used it give new proofs of other important results in representation theory established in the 70's. In 2002 Iyama showed that every finite-dimensional algebra has finite representation dimension, thus answering a question with more than 30 years, posed by Auslander. In this talk we present yet another application of the Gabriel-Roiter measure, namely we use it to provide a new proof of the finiteness of the representation dimension.

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