Auslander-Reiten quivers and the Coxeter complex
量子代数
2007-05-23 v1 环与代数
摘要
Let Q be a quiver of type ADE. We construct the corresponding Auslander-Reiten quiver as a topological complex inside the Coxeter complex associated with the underlying Dynkin diagram. We use the notion of chamber weights coming from the theory of the canonical basis of quantized envelopping algebras, and show this set has a special linearity property in our setting. Finally, we consider A_n case, and describe how Auslander-Reiten quivers correspond to particular wiring diagrams.
引用
@article{arxiv.math/0208098,
title = {Auslander-Reiten quivers and the Coxeter complex},
author = {Shmuel Zelikson},
journal= {arXiv preprint arXiv:math/0208098},
year = {2007}
}
备注
19 pages. Revised version of SDAD preprint 2001-25. Submitted to Algebra and Representation Theory. LaTeX2e, uses epic, eepic packages