Tilting modules for the Auslander algebra of \(K[x]/(x^n)\)

We construct an isomorphism between the partially ordered set of tilting modules for the Auslander algebra of \(K[x]/(x^n)\) and the interval of rational permutation braids in the braid group on \(n\) strands. Hence, there are only finitely many tilting modules.

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Bibliographic Details
Published in:arXiv.org 2018-03
Main Author: Geuenich, Jan
Format: Article
Language:English
Subjects:
Braid theory
Braiding
Isomorphism
Modules
Permutations
Online Access:Get full text
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Summary:We construct an isomorphism between the partially ordered set of tilting modules for the Auslander algebra of \(K[x]/(x^n)\) and the interval of rational permutation braids in the braid group on \(n\) strands. Hence, there are only finitely many tilting modules.
ISSN:2331-8422