Large tilting modules and representation type

Details Large tilting modules and representation type Large tilting modules and representation type

2008-04-04

arxiv.org/abs/0804.0815v1

Mathematics

Representation Theory

14 pages

Scientific paper

We study finiteness conditions on large tilting modules over arbitrary rings. We then turn to a hereditary artin algebra R and apply our results to the (infinite dimensional) tilting module L that generates all modules without preprojective direct summands. We show that the behaviour of L over its endomorphism ring determines the representation type of R. A similar result holds true for the (infinite dimensional) tilting module W that generates the divisible modules. Finally, we extend to the wild case some results on Baer modules and torsion-free modules proven in [AHT] for tame hereditary algebras.

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