Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
This information is intended exclusively for students already enrolled in this course.If you are a new student interested in enrolling, you can find information about the course of study on the course page:
Laurea magistrale in Mathematics - Enrollment from 2025/2026The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
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1 module between the following1 module between the following 3 modules among the followingLegend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Representation theory (2020/2021)
Teaching code
4S001099
Academic staff
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/02 - ALGEBRA
Period
II semestre dal Mar 1, 2021 al Jun 11, 2021.
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.
Program
The entire course will be available online. In addition, all the lessons will be held in-class.
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.
The course consists of front lessons and classroom exercises. Moreover optional tutoring activities are offered. In particular, weekly home exercises are given. They are individually corrected by a tutor and discussed during the exercise hours.
| Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|
| 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 |
Examination Methods
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.
The exam is aimed at verifying the full maturity of demonstrative techniques and the ability to read and understand advanced topics of representation theory.
The assessment methods could change according to the academic rules. The remote mode is however guaranteed for all students who will ask for it in the academic year 2020/21.
