Fusion Quivers

2023/07/18 by Schaumann, Gregor
#Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2307.09229

Abstract

We develop a categorical approach to quivers and their modules. Naturally this leads to a notion of an action of a monoidal category on quivers. Using this, we construct for a large class of quivers rigid monoidal structures on their categories of modules. This fusion product on the quiver modules induces a graded ring structure with duality and trace on the moduli spaces of semisimple quiver modules. Our approach allows to consider a class of relations on such fusion quivers that are compatible with the rigid monoidal structure. In particular we obtain a class of preprojective algebras with fusion product on their modules.

Related

• Rigid integral representations of quivers over arbitrary commutative rings
• Category equivalences involving graded modules over path algebras of quivers
• Classification of finite type fusion quivers
• Relative homological algebra in categories of representations of infinite quivers
• Coxeter quiver representations in fusion categories and Gabriel's theorem