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Tilting theory and cluster combinatorics
| Venue: | 572–618. EQUIVALENCE AND GRADED DERIVED EQUIVALENCE 43 |
| Citations: | 129 - 8 self |
BibTeX
@INPROCEEDINGS{Buan_tiltingtheory,
author = {Aslak Bakke Buan and Robert Marsh and Markus Reineke and Idun Reiten},
title = {Tilting theory and cluster combinatorics},
booktitle = {572–618. EQUIVALENCE AND GRADED DERIVED EQUIVALENCE 43},
year = {}
}
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Abstract
of a finite-dimensional hereditary algebra H over a field. We show that, in the simply-laced Dynkin case, C can be regarded as a natural model for the combinatorics of the corresponding Fomin–Zelevinsky cluster algebra. In this model, the tilting objects correspond to the clusters of Fomin–Zelevinsky. Using approximation theory, we investigate the tilting theory of C, showing that it is more regular than that of the module category itself, and demonstrating an interesting link with the classification of self-injective algebras of finite representation type. This investigation also enables us to conjecture a generalisation of APR-tilting.
