Proof of the tree module property for exceptional representations of tame quivers

Abstract

This document serves as an arXiv entry point for the appendix to the paper [13] (the ancillary file e6_proof.pdf -- ``Proof of the tree module property for exceptional representations of the quiver ${\tilde{\mathbb{E}}}_6$'') and the appendix to the paper [12] (the ancillary file d6_proof.pdf -- ``Proof of the tree module property for exceptional representations of the quiver ${\tilde{\mathbb{D}}}_6$''). The ancillary files contain the computer generated part of the proofs of the main results in [13] respectively [12], giving a complete and general list of tree representations corresponding to exceptional modules over the path algebra of the canonically oriented Euclidean quiver ${\tilde{\mathbb{E}}}_6$, respectively ${\tilde{\mathbb{D}}}_6$. The proofs (involving induction and symbolic computation with block matrices) were partially generated by a purposefully developed computer software, outputting in a detailed step-by-step fashion as if written ``by hand''. We also give here a short theoretical introduction and an overview of the computational method used to prove the formulas given in the papers [13] and [12].

8 pages, with ancillary documents (e6_proof.pdf and d6_proof.pdf)

References in corpus (3)

• Indecomposable representations for extended Dynkin quivers
• Schofield sequences in the Euclidean case
• The dimensions of the homomorphism spaces to indecomposable modules over the four subspace algebra