We develop a structure theory for two classes of infinite dimensional modules over tame hereditary algebras: the Baer modules, and the Mittag–Leffler ones. We show that a module M is Baer iff M is p–filtered where p is the preprojective component of the tame hereditary algebra R. We apply this to prove that the universal localization of a Baer module is projective in case we localize with respect to a complete tube. Using infinite dimensional tilting theory we then obtain a structure result showing that Baer modules are more complex then the (infinite dimensional) preprojective modules. In the final section, we give a complete classification of the Mittag–Leffler modules.
Baer and Mittag-Leffler modules over tame hereditary artin algebras
ANGELERI, LIDIA;
2010-01-01
Abstract
We develop a structure theory for two classes of infinite dimensional modules over tame hereditary algebras: the Baer modules, and the Mittag–Leffler ones. We show that a module M is Baer iff M is p–filtered where p is the preprojective component of the tame hereditary algebra R. We apply this to prove that the universal localization of a Baer module is projective in case we localize with respect to a complete tube. Using infinite dimensional tilting theory we then obtain a structure result showing that Baer modules are more complex then the (infinite dimensional) preprojective modules. In the final section, we give a complete classification of the Mittag–Leffler modules.
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