The Ingalls-Thomas Bijections

Given a finite acyclic quiver Q with path algebra kQ, Ingalls and Thomas have exhibited a bijection between the set of Morita equivalence classes of support-tilting modules and the set of thick subcategories of mod kQ and they have collected a large number of further bijections with these sets. We a...

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Bibliographic Details
Published in:arXiv.org 2015-11
Main Authors: Obaid, Mustafa A A, S Khalid Nauman, Fakieh, Wafaa M, Ringel, Claus Michael
Format: Article
Language:English
Subjects:
Algebra
Online Access:Get full text
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Summary:Given a finite acyclic quiver Q with path algebra kQ, Ingalls and Thomas have exhibited a bijection between the set of Morita equivalence classes of support-tilting modules and the set of thick subcategories of mod kQ and they have collected a large number of further bijections with these sets. We add some additional bijections and show that all these bijections hold for arbitrary hereditary artin algebras. The proofs presented here seem to be of interest also in the special case of the path algebra of a quiver.
ISSN:2331-8422