The finite EI categories of Cartan type
Representation Theory
2019-01-15 v2 Rings and Algebras
Abstract
To each symmetrizable Cartan matrix, we associate a finite free EI category. We prove that the corresponding category algebra is isomorphic to the algebra defined in [C. Geiss, B. Leclerc, and J. Schr\"{o}er, Quivers with relations for symmetrizable Cartan matrices I: Foundations, Invent. Math. 209 (2017), 61--158], which is associated to another symmetrizable Cartan matrix. In certain cases, the algebra isomorphism provides an algebraic enrichment of the well-known correspondence between symmetrizable Cartan matrices and graphs with automorphisms.
Keywords
Cite
@article{arxiv.1811.00294,
title = {The finite EI categories of Cartan type},
author = {Xiao-Wu Chen and Ren Wang},
journal= {arXiv preprint arXiv:1811.00294},
year = {2019}
}
Comments
18 pages; a new version of arXiv: 1811.00294