## The tilting module of a AR-quiver

Given a quiver and its AR quiver expressed by dimension vector,how to find the tilting module of it?When we check it is a tilting module,we should computer the Hom and Ext functor and AR transtion from the AR quiver expressed by dimension vector,how to do it?

Assem's book:Elements of the Representation Theory of Associative Algebras Vol1,Chapter VI,example 2.8 is associated with this question,you can explain it as an example or give a new example.

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 For a given algebra there are often many different tilting modules, especially if you allow $\rm{pd} T < \infty$ and not just $\rm{pd} T \leq 1$. Are you asking how to find the AR quiver, or how to check if something is a tilting module? – Dag Oskar Madsen Aug 24 at 10:54