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Recollements of abelian categories and ideals in heredity chains--a recursive approach to quasi-hereditary algebras


Authors: Nan Gao, Steffen Koenig and Chrysostomos Psaroudakis
Journal: Proc. Amer. Math. Soc. 147 (2019), 4625-4637
MSC (2010): Primary 16G10; Secondary 17B10, 16E60, 18G15
DOI: https://doi.org/10.1090/proc/14620
Published electronically: July 1, 2019
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Abstract: Recollements of abelian categories are used as a basis of a homological and recursive approach to quasi-hereditary algebras. This yields a homological proof of Dlab and Ringel's characterisation of idempotent ideals occurring in heredity chains, which in turn characterises quasi-hereditary algebras recursively. Further applications are given to hereditary algebras and to Morita context rings.


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Additional Information

Nan Gao
Affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China
Email: nangao@shu.edu.cn

Steffen Koenig
Affiliation: Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
Email: skoenig@mathematik.uni-stuttgart.de

Chrysostomos Psaroudakis
Affiliation: Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
Address at time of publication: Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece
Email: chpsaroud@math.auth.gr

DOI: https://doi.org/10.1090/proc/14620
Received by editor(s): April 25, 2018
Received by editor(s) in revised form: February 10, 2019
Published electronically: July 1, 2019
Additional Notes: The first named author was supported by the National Natural Science Foundation of China (grant No. 11771272)
The third named author was supported by Deutsche Forschungsgemeinschaft (DFG, grant KO $1281/14-1$)
Communicated by: Jerzy Weyman
Article copyright: © Copyright 2019 American Mathematical Society