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 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:Communications in algebra 2022-01, Vol.50 (1), p.82-95
Main Author: Geuenich, Jan
Format: Article
Language:English
Subjects:
Auslander algebra
braid group
Braid theory
Braiding
Isomorphism
Modules
Permutations
tilting theory
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Description
Summary:We construct an isomorphism between the partially ordered set of tilting modules for the Auslander algebra of and the interval of rational permutation braids in the braid group on n strands. Hence, there are only finitely many tilting modules.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2021.1951748