Serial functors, Jacobson radical and representation type

✍ Scribed by Mike Prest; Jan Schröer

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 123 KB
• Volume: 170
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(01)00133-5

✦ Synopsis

It is an important problem in representation theory to relate the representation type of a k-algebra A to dimensions of ÿnitely presented functors from mod(A) to mod(k). We prove that a string algebra is of domestic representation type if and only if the dimension of all serial functors in the associated category of ÿnitely presented functors is ÿnite. Using the 'hammock approach' we provide explicit examples of serial functors.