This page contains a list of books on representation theory of finite-dimensional algebras and a selection of related topics. This page is under construction. If you have any suggestions, feel free to email Rosanna Laking or Julian Külshammer.
Introductory textbooks
This is a selection of introductory textbooks focused on representation theory of finite-dimensional algebras and quivers.
- Assem, Coelho: Basic representation theory of algebras, 2020. (MR4180681, Zbl 1451.16001)
- Assem, Simson, Skowroński: Elements of the representation theory of associative algebras, Vol. 1, 2006. (MR2197389, Zbl 1092.16001)
- Auslander, Reiten, Smalø: Representation theory of Artin algebras, 1995. (MR147667, Zbl 0834.16001)
- Barot: Introduction to the representation theory of algebras, 2015. (MR3309698, Zbl 1330.16001)
- Derksen, Weyman: An introduction to quiver representations, 2017. (MR3727119, Zbl 1426.16001)
- Drozd, Kirichenko: Finite dimensional algebras, 1994. (MR1284468, Zbl 0816.16001)
- Erdmann, Holm: Algebras and representation theory, 2018. (MR3837168, Zbl 1429.16001)
- Gabriel, Roiter: Representations of finite dimensional algebras, 1992. (MR1475926)
- Krause: Homological theory of representations, 2021. (MR4327095, Zbl 07407039)
- Schiffler: Quiver representations, 2014. (MR3308668, Zbl 1310.16015)
More general textbooks
This section contains textbooks which consider representations of finite-dimensional algebras but have a slightly different focus.
- Benson: Representations and cohomology I & II, 1998. (MR1644252, Zbl 0908.20001)
- Deng, Du, Parshall, Wang: Finite dimensional algebras and quantum groups, 2008. (MR2457938, Zbl 1154.17003)
- Etingof et al: Introduction to representation theory, 2011. (pdf, MR2808160, Zbl 1242.20001)
- Pierce: Associative algebras, 1982. (MR0674652, 0497.16001)
- Zimmermann: Representation theory – A homological algebra point of view, 2014 (MR3289041, 1306.20001)
Lecture notes and other resources
The following lecture notes provide a useful introduction to various aspects of the representation theory of finite-dimensional algebras.
- An introduction to Auslander–Reiten theory by Lidia Angeleri Hügel
- Lectures on representations of quivers by Bill Crawley-Boevey
- More lectures on representations of quivers by Bill Crawley-Boevey
- FD-Atlas by Jan Schröer
Software
The following is a list of software that is available for making calculations related to finite-dimensional algebras.
- Quivers and Path Algebras (QPA) administered by the QPA-team
- Quiver mutations created by Bernhard Keller
- String applet created by Jan Geuenich