Representation theory (2012/2013)

Course code
4S001099
Credits
6
Coordinator
Lidia Angeleri
Academic sector
MAT/02 - ALGEBRA
Language of instruction
Italian
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
Teoria 5 I semestre Lidia Angeleri
Francesca Mantese
Esercitazioni 1 I semestre Dirk Kussin

Lesson timetable

I semestre
Activity Day Time Type Place Note
Teoria Tuesday 11:30 AM - 1:30 PM lesson Lecture Hall M  
Teoria 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.

Assessment methods and criteria

The exam consists of a written examination and of an optional oral examination.

Teaching aids
Title Format (Language, Size, Publication date)
BIBLIOGRAPHY  pdfpdf (it, 70 KB, 28/09/12)
COURSE ORGANIZATION  pdfpdf (it, 52 KB, 28/09/12)
Esercizi - Foglio 1  pdfpdf (it, 88 KB, 25/10/12)
Esercizi - Foglio 2  pdfpdf (it, 96 KB, 09/11/12)
Esercizi - Foglio 3  pdfpdf (it, 99 KB, 18/11/12)
Esercizi - Foglio 4  pdfpdf (it, 103 KB, 13/12/12)
Esercizi - Foglio 5  pdfpdf (it, 59 KB, 17/01/13)
note corso  pdfpdf (it, 243 KB, 09/11/12)
note corso - parte 2  pdfpdf (it, 531 KB, 23/01/13)
vecchi esami  pdfpdf (it, 84 KB, 10/01/13)
vecchi esami - soluzioni 1  pdfpdf (it, 1546 KB, 10/01/13)
vecchi esami - soluzioni 2  pdfpdf (it, 824 KB, 10/01/13)

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

Data from AA 2012/2013 are not available yet