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Auslander–Reiten Theory for Finite-Dimensional Algebras

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Homological Methods, Representation Theory, and Cluster Algebras

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Abstract

This article is based on a course given at the CIMPA School “Homological Methods, Representation Theory and Cluster Algebras,” held in March 2016 in Mar del Plata. The aim of the course, consisting of four lectures, was to provide a brief introduction to the notion of an almost split sequence and its use in the representation theory of finite-dimensional algebras. The first two sections are reduced, and the next three sections are extended in comparison with the above-mentioned course.

Dedicated to María Inés Platzeck on the occasion of her 70th birthday

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Acknowledgements

This work was completed with the support of the research grant from the National Science Center, Poland, DEC-2011/02/A/ST1/00216.

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  1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100, Toruń, Poland

    Piotr Malicki

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  1. Piotr Malicki
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  1. Département de Mathématiques, Université de Sherbrooke, Sherbrooke, Québec, Canada

    Ibrahim Assem

  2. Centro Marplatense de Investigaciones Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Mar del Plata, Buenos Aires, Argentina

    Sonia Trepode

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Malicki, P. (2018). Auslander–Reiten Theory for Finite-Dimensional Algebras. In: Assem, I., Trepode, S. (eds) Homological Methods, Representation Theory, and Cluster Algebras. CRM Short Courses. Springer, Cham. https://doi.org/10.1007/978-3-319-74585-5_2

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