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- W4312004096 abstract "$Q$ is a quiver of type $tilde A(n-1,1)$ if its graph is of affine type $tilde A_{n-1}$ and if its arrows have a certain orientation. We develop a bijection between the set of indecomposable $kQ$-modules whose dimension vectors are positive real roots of the root system associated to $Q$ and a certain set of planar curves. We prove that the number of self-intersections of the curve which corresponds to the module $M$ is equal to the dimension of $text{Ext}^1_{kQ}(M,M)$. We also prove that, for many pairs of modules $(M,N)$, the number of intersections between the corresponding two curves is equal to the dimension of $text{Ext}^1_C (M,N)$, where $C$ is the cluster category of $kQ$-mod." @default.
- W4312004096 created "2023-01-03" @default.
- W4312004096 creator A5028280094 @default.
- W4312004096 date "2021-11-24" @default.
- W4312004096 modified "2023-09-27" @default.
- W4312004096 title "Computation of extension spaces for the path algebra of type $tilde A(n-1,1)$ using planar curves" @default.
- W4312004096 doi "https://doi.org/10.48550/arxiv.2111.12630" @default.
- W4312004096 hasPublicationYear "2021" @default.
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