Geodesic
DISTRIBUTIVE LATTICES OF TILTING MODULES AND SUPPORT τ-TILTING MODULES OVER PATH ALGEBRAS
Glasgow mathematical journal, Tome 59 (2017) no. 2, pp. 503-511

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DOI

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 $\mathbb{A}_{1}$ . 
YANG, YICHAO. DISTRIBUTIVE LATTICES OF TILTING MODULES AND SUPPORT τ-TILTING MODULES OVER PATH ALGEBRAS. Glasgow mathematical journal, Tome 59 (2017) no. 2, pp. 503-511. doi: 10.1017/S001708951600032X
@article{10_1017_S001708951600032X,
     author = {YANG, YICHAO},
     title = {DISTRIBUTIVE {LATTICES} {OF} {TILTING} {MODULES} {AND} {SUPPORT} {\ensuremath{\tau}-TILTING} {MODULES} {OVER} {PATH} {ALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {503--511},
     year = {2017},
     volume = {59},
     number = {2},
     doi = {10.1017/S001708951600032X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951600032X/}
}
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