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On Categorifications of Non-Integer Quivers

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CAR - Cluster algebras and representation theory

Suppose we have a skew-symmetric matrix with real (non-integer) entries. We may apply the usual rules of mutation on such a matrix and its corresponding quiver (with real-weighted arrows). There is a nice categorical interpretation of integer quivers and their mutations via the cluster category, which begs the question as to whether a similar categorical interpretation exists for real-weighted quivers and their mutations. In this talk, we will present such a categorification for real-weighted quivers that are associated to Coxeter diagrams of types H_3, H_4 and I_2(2n+1) via the theory of weighted (un)foldings and semiring actions on the module, derived and cluster categories of ADE -quivers.

This talk is part of the Isaac Newton Institute Seminar Series series.

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