A Characterization of Finite EI Categories with Hereditary Category Algebras

Details A Characterization of Finite EI Categories with Hereditary Category Algebras A Characterization of Finite EI Categories with Hereditary Category Algebras

2011-03-04

arxiv.org/abs/1103.0959v1

Mathematics

Representation Theory

40 pages

Scientific paper

In this paper we give an explicit algorithm to construct the ordinary quiver of a finite EI category for which the endomorphism groups of all objects have orders invertible in the field k. We classify all finite EI categories with hereditary category algebras, characterizing them as free EI categories (in a sense which we define) for which all endomorphism groups of objects have invertible orders. Some applications on the representation types of finite EI categories are derived.

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