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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Tilting modules over tame hereditary algebras

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Author(s):
Huegel, Lidia Angeleri [1] ; Sanchez, Javier [2]
Total Authors: 2
Affiliation:
[1] Univ Verona, Dipartimento Informat, Settore Matemat, I-37134 Verona - Italy
[2] Univ Sao Paulo, Dept Math IME, BR-05314970 Sao Paulo - Brazil
Total Affiliations: 2
Document type: Journal article
Source: JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK; v. 682, p. 1-48, SEP 2013.
Web of Science Citations: 9
Abstract

We give a complete classification of the infinite dimensional tilting modules over a tame hereditary algebra R. We start our investigations by considering tilting modules of the form T = R-U circle plus R-U/R where U is a union of tubes, and R-U denotes the universal localization of R at U in the sense of Schofield and Crawley-Boevey. Here R-U/R is a direct sum of the Prufer modules corresponding to the tubes in U. Over the Kronecker algebra, large tilting modules are of this form in all but one case, the exception being the Lukas tilting module L whose tilting class Gen L consists of all modules without indecomposable preprojective summands. Over an arbitrary tame hereditary algebra, T can have finite dimensional summands, but the infinite dimensional part of T is still built up from universal localizations, Prufer modules and (localizations of) the Lukas tilting module. We also recover the classification of the infinite dimensional cotilting R-modules due to Buan and Krause. (AU)

FAPESP's process: 09/50886-0 - Embedding group algebras and crossed products in division rings
Grantee:Javier Sanchez Serda
Support type: Scholarships in Brazil - Post-Doctorate