Titlebook: Homological Methods, Representation Theory, and Cluster Algebras; Ibrahim Assem,Sonia Trepode Textbook 2018 Springer International Publish

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Cluster Characters,cluster algebras became apparent in, for instance, (R. Marsh, M. Reineke and A. Zelevinsky (2003). Trans. Amer. Math. Soc. 355(10), 4171–4186.) [.], (A.B Buan, R. Marsh, M. Reineke, I. Reiten and G. Todorov (2006). Adv. Math. 204(2), 572–618.) [.], (P. Caldero and F. Chapoton (2006). Comment. Math. Helv. 81(3), 595–616.) [.].

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2522-5200 searchers, and research mathematicians.Assumes minimal previ.This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text

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Brauer Graph Algebras,rived equivalences of Brauer graph algebras with derived equivalences of frozen Jacobian algebras is the topic of the next section. In the last section, after defining Green’s walk around the Brauer graph, a complete description of the Auslander Reiten quiver of a Brauer graph algebra is given.

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Introduction to the Representation Theory of Finite-Dimensional Algebras: The Functorial Approach, 2016. The aim of this brief course is to give an introduction to the functorial approach to the representation theory of finite-dimensional algebras, developed by Maurice Auslander and Idun Reiten, and is strongly based on the work “A functorial approach to representation theory,” by M.?Auslander (

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