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arXiv 2001.00016math.RTcs.SC
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Tame箭图例外表示的树模性质的证明

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

Szabolcs Lénárt, Ábel Lőrinczi, Csaba Szántó, István Szöllősi

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

本文档作为论文附录[13]（辅助文件e6_proof.pdf --"Proof of the tree module property for exceptional representations of the $\widetilde{\mathbb{E}}_6$ $\widetilde{\mathbb{E}}_6$“）和论文附录[12]（辅助文件d6_proof.pdf --" Proof the tree module property for exceptional representations of the $\widetilde{\mathbb{D}}_6$ $\widetilde{\mathbb{D}}_6$”）的arXiv入口点。辅助文件包含计算机生成的部分证明的主要结果在[13]分别[12]，给出了一个完整的和一般的列表树表示对应的例外模块的路径代数的规范定向欧几里德矩阵$\widetilde{\mathbb{E}}_6$，分别$\widetilde{\mathbb{D}}_6$。证明（包括归纳法和使用分块矩阵的符号计算）部分由专门开发的计算机软件生成，以详细的逐步方式输出，就像“手工”写的一样。本文还简要介绍了文献[13]和[12]中公式的理论证明和计算方法。

英文摘要：

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 $\widetilde{\mathbb{E}}_6$'') 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 $\widetilde{\mathbb{D}}_6$''). 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 $\widetilde{\mathbb{E}}_6$, respectively $\widetilde{\mathbb{D}}_6$. 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].

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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