Representation theory (2018/2019)



Course code
4S001099
Credits
6
Coordinator
Lidia Angeleri
Academic sector
MAT/02 - ALGEBRA
Language of instruction
English
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
Teoria 1 2 II semestre Francesca Mantese

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Teoria 2 3 II semestre Lidia Angeleri

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Esercitazioni 1 II semestre Rosanna Laking

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Learning outcomes

The course provides a first introduction to the representation theory of quivers, an important branch of modern algebra with connections to geometry, topology and theoretical physics.

Syllabus

Quivers, representations, the path algebra. Categories and functors, module categories. Filtrations: Theorems of Schreier and Jordan-Hoelder. Direct sum decomposition, theorem of Krull-Remak-Schmidt. Homological algebra: pushout, pullback, Ext, complexes, homology. Auslander-Reiten-theory. Algebras of finite and of tame representation type.

Assessment methods and criteria

The exam consists of a written examination. The mark obtained in the written examination can be improved by the mark obtained for the homework and/or by an optional oral examination. Only students who have passed the written exam will be admitted to the oral examination.

Reference books
Activity Author Title Publisher Year ISBN Note
Teoria 1 J.J. Rotman An introduction to homological algebra (Edizione 2) Academic Press 2009 0-12-599250-5
Teoria 1 I. Assem, D. Simson, A. Skowronski Elements of the representation theory of associative algebras Cambridge University Press 2006
Teoria 1 M.Auslander, I.Reiten, S.O. Smalø Representation theory of artin algebras (Edizione 2) Cambridge University Press 1997
Teoria 1 F.W. Anderson, K.R. Fuller Rings and categories of modules (Edizione 2) Springer 1992
Teoria 2 Joseph J. Rotman An introduction to homological algebra Academic Press  
Teoria 2 I. Assem, D. Simson, A. Skowronski Elements of the representation theory of associative algebras Cambridge University Press 2006
Teoria 2 M.Auslander, I.Reiten, S.O. Smalø Representation theory of artin algebras (Edizione 2) Cambridge University Press 1997
Teoria 2 F.W. Anderson, K.R. Fuller Rings and categories of modules (Edizione 2) Springer 1992
Teaching aids
Title Format (Language, Size, Publication date)
Exercises 1  pdfpdf (it, 143 KB, 15/03/19)
Notes (28/03)  pdfpdf (en, 383 KB, 28/03/19)
Lecture notes  pdfpdf (it, 757 KB, 02/06/19)

STUDENT MODULE EVALUATION - 2017/2018