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arXiv · 1811.00294

The finite EI categories of Cartan type

Xiao-Wu Chen·Ren Wang
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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.

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Xiao-Wu Chen, Ren Wang. 2018-11-01. The finite EI categories of Cartan type. https://arxiv.org/abs/1811.00294

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