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arXiv · 1505.07497

Distributive lattices of tilting modules and support $τ$-tilting modules over path algebras

Yichao Yang
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Abstract

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 nonlinear orientation and the second poset is a distributive lattice if and only if $Q$ is of type $\mathbb{A}_{1}$.

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Yichao Yang. 2015-05-27. Distributive lattices of tilting modules and support $τ$-tilting modules over path algebras. https://arxiv.org/abs/1505.07497

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