Gabriel-Roiter measure for finite dimensional algebras

• Applicant: Dr. Bo Chen
• Subject Area: Mathematics
• Term: from 2009 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 127141831

The main goals of representation theory of finite dimensional algebras are to determine the representation type (finite/tame/wild) of an algebra and to describe its module category (representations, morphisms, and homological properties of the category). The main tool nowadays is the so-called Auslander-Reiten theory. The subject of this new proposal is the Gabriel-Roiter measure, which had been used by Roiter in his proof of the fundamental Brauer-Thrall conjecture I, dealing with algebras of finite type. Recently, Ringel has suggested to develop the Gabriel-Roiter measure into a foundational tool for representation theory of algebras of any representation type, thus providing alternative methods to those of Auslander-Reiten theory. So far, however, results have been obtained mainly on the Gabriel-Roiter measure in the case of algebras of finite representation type. Building on some first results I have obtained for tame hereditary algebras, I am planning to extend the theory of Gabriel-Roiter measure to wild algebras, concentrating on wild hereditary algebras that are of interest for example in applications to Lie theory.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1388: Representation Theory