ON Δ-GOOD MODULE CATEGORIES ARISING FROM HEREDITARY ALGEBRAS

Abstract

Let A be a hereditary artin algebra and M a complete exceptional sequence over A. Let F(M) be the subcategory of A-mod consisting of modules with an M-filtration. A quasi-hereditary algebra is called e-quasi-hereditary provided that its Δ-good module category is equivalent to the category F(M) under an exact functor. A characterization of e-quasi-hereditary algebras is given, and a connection between the representation type of F(Δ) and the Tits form associated to it for some e-quasi-hereditary algebras is obtained in this paper.

ACKNOWLEDGMENTS

I am very grateful to the referee for his or her careful suggestions to improve the manuscript. I would like to thank Xueqing Chen at Carleton University for his proof-reading. This project was supported by NSF 10001017 and China Postdoctoral Science Foundation.