APR tilting modules and graded quivers with potential

Details APR tilting modules and graded quivers with potential APR tilting modules and graded quivers with potential

2011-12-19

arxiv.org/abs/1112.4266v1

Mathematics

Representation Theory

18 pages

Scientific paper

We study the quiver with relations of the endomorphism algebra of an APR tilting module. We give an explicit description of the quiver with relations by graded quivers with potential (QPs) and mutations. The result also implies that mutations of QPs with algebraic cuts induce tilting mutations between the associated truncated Jacobian algebras. Consequently, mutations of QPs provide a rich source of derived equivalence classes of algebras. As an application, we give a sufficient condition of QPs such that Derksen-Weyman-Zelevinsky's question has a positive answer.

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