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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three course to be chosen among the following
A course to be chosen among the following
Legend | 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 (2014/2015)
Teaching code
4S001099
Academic staff
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/02 - ALGEBRA
Period
I sem. dal Oct 1, 2014 al Jan 30, 2015.
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
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.
Author | Title | Publishing house | Year | ISBN | Notes |
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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 |
Examination Methods
The exam consists of a written examination and of an optional oral examination. There will be an intermediate test in November.
Teaching materials e documents
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BIBLIOGRAPHY (pdf, it, 70 KB, 9/26/14)
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Exercises December 2014 (pdf, it, 101 KB, 12/10/14)
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Exercises January 2015 (pdf, it, 103 KB, 1/17/15)
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Exercises November 2014 (pdf, it, 152 KB, 11/25/14)
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Introduction to the representation theory of quivers - notes part 2 (pdf, it, 539 KB, 1/22/15)
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old exam 1 - solutions (pdf, it, 1546 KB, 1/17/15)
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old exam 2 - solutions (pdf, it, 824 KB, 1/17/15)
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old exams (pdf, it, 84 KB, 1/17/15)
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Organization of the course (pdf, it, 51 KB, 11/16/14)
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Quivers, algebras and representations - Notes part 3 (pdf, it, 1213 KB, 11/28/14)
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Rings and Modules - Notes part 1 (pdf, it, 328 KB, 11/28/14)