Representation theory (2014/2015)

Course code
4S001099
Name of lecturers
Lidia Angeleri, Francesca Mantese
Coordinator
Lidia Angeleri
Number of ECTS credits allocated
6
Academic sector
MAT/02 - ALGEBRA
Language of instruction
English
Period
I sem. dal Oct 1, 2014 al Jan 30, 2015.

Lesson timetable

I sem.
Day Time Type Place Note
Tuesday 11:30 AM - 1:30 PM lesson Lecture Hall M  
Thursday 9:30 AM - 11:30 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
T.Y. Lam A first course in noncommutative rings (Edizione 2) Springer 2001 0-387-95183-0
J.J. Rotman An introduction to homological algebra (Edizione 2) Academic Press 2009 0-12-599250-5
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 and of an optional oral examination. There will be an intermediate test in November.

Teaching aids

Documents

Student opinions - 2014/2015


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

Statistics
Outcomes Exams Outcomes Percentages Average Standard Deviation
Positive 50.0% 22 3
Rejected 18.75%
Absent 31.25%
Ritirati --
Canceled --
Distribuzione degli esiti positivi
18 19 20 21 22 23 24 25 26 27 28 29 30 30 e Lode
25.0% 0.0% 12.5% 0.0% 12.5% 25.0% 12.5% 0.0% 0.0% 0.0% 12.5% 0.0% 0.0% 0.0%

Data from AA 2014/2015 based on 16 students. I valori in percentuale sono arrotondati al numero intero più vicino.