Representation theory (2016/2017)

Course code
4S001099
Name of lecturers
Lidia Angeleri, David Pauksztello
Coordinator
Lidia Angeleri
Number of ECTS credits allocated
6
Academic sector
MAT/02 - ALGEBRA
Language of instruction
English
Period
I sem. dal Oct 3, 2016 al Jan 31, 2017.

Lesson timetable

I sem.
Day Time Type Place Note
Tuesday 8:30 AM - 10:30 AM lesson Lecture Hall M  
Tuesday 1:30 PM - 3:30 PM lesson Lecture Hall M from Nov 8, 2016  to Nov 15, 2016
Thursday 8:30 AM - 10:30 AM lesson Lecture Hall M  

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.

Reference books
Author Title Publisher Year ISBN Note
Joseph J. Rotman An introduction to homological algebra Academic Press  
I. Assem, D. Simson, A. Skowronski Elements of the representation theory of associative algebras Cambridge University Press 2006
M.Auslander, I.Reiten, S.O. Smalø Representation theory of artin algebras (Edizione 2) Cambridge University Press 1997
F.W. Anderson, K.R. Fuller Rings and categories of modules (Edizione 2) Springer 1992

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.

Teaching aids

Documents

Student opinions - 2015/2016


Statistics about transparency requirements (Attuazione Art. 2 del D.M. 31/10/2007, n. 544)

Data from AA 2016/2017 are not available yet