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DISTRIBUTIVE LATTICES OF TILTING MODULES AND SUPPORT τ-TILTING MODULES OVER PATH ALGEBRAS

Part of: Representation theory of rings and algebras Algebraic combinatorics

Published online by Cambridge University Press:  10 June 2016

YICHAO YANG
YICHAO YANG*
Affiliation:
Département de mathématiques, Université de Sherbrooke, Sherbrooke, Québec, Canada, J1K 2R1 E-mail: yichao.yang@usherbrooke.ca
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Abstract

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In this paper, we study the poset of basic tilting kQ-modules when Q is a Dynkin quiver, and the poset of basic support τ-tilting kQ-modules when Q is a connected acyclic quiver respectively. It is shown that the first poset is a distributive lattice if and only if Q is of types $\mathbb{A}_{1}$, $\mathbb{A}_{2}$ or $\mathbb{A}_{3}$ with a non-linear orientation and the second poset is a distributive lattice if and only if Q is of type $\mathbb{A}_{1}$.

MSC classification

Primary: 16G20: Representations of quivers and partially ordered sets
Secondary: 16G70: Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers 05E10: Combinatorial aspects of representation theory
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 2 , May 2017 , pp. 503 - 511
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

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