MTK729 - INTRODUCTION TO REPRESENTATION THEORY of ALG. I

Course Name Code Semester Theory
(hours/week)		 Application
(hours/week)		 Credit ECTS
INTRODUCTION TO REPRESENTATION THEORY of ALG. I MTK729 1st Semester 3 0 3 12
Prequisitesnone
Course languageTurkish
Course typeElective 
Mode of DeliveryFace-to-Face 
Learning and teaching strategiesLecture
Discussion
Question and Answer
Other: Assignment  
Instructor (s)Assoc. Prof. Dr. Bülent Saraç 
Course objectiveThe aim of this course is to help students interpret and apply the fundamental concepts and results given in the representation theory of associative algebras. 
Learning outcomes
  1. By the end of this course, the student identifies the concepts of algebra and module, describes projective and injective modules over finite dimensional algebras, identifies basic algebras and realizes Morita equivalences,
  2. identifies quivers and path algebras,
  3. describes finite dimensional algebras in terms of quivers,
  4. identifies quiver representations,
  5. realizes the correspondence between quiver representations and modules,
  6. identifies the dimension vector of a module and Euler characteristi of an algebra,
  7. evaluates irreducible morphisms and almost split sequences,
  8. grasps Auslander-Reiten translations, describes the Auslander-Reiten quiver of an algebra, approaches almost split sequences with functors.
Course Content Algebras and modules
Quivers and algebras
Representations and modules
Auslander-Reiten Theory
 
References1) I. Assem, D. Simson, A. Skowroski, Elements of the representation theory of associative algebras. Vol. 1. Techniques of representation theory. London Mathematical Society Student Texts, 65. Cambridge University Press, Cambridge, 2006.
2) M. Barot, Introduction to the representation theory of algebras. Springer, Cham, 2015.
3) M. Auslander, I. Reiten, S. O. Smalø, Representation theory of Artin algebras. Cambridge Studies in Advanced Mathematics, 36. Cambridge University Press, Cambridge, 1995.
 

Course outline weekly

WeeksTopics
Week 1Algebras and modules
Week 2Semisimple modules and the radical of a module, Direct sum decompositions
Week 3Projective and injective modules, basic algebras and embeddings of module categories
Week 4Quivers and path algebras
Week 5Admissible ideals and quotients of the path algebra
Week 6Midterm exam
Week 7Representations of bound quivers
Week 8The simple, projective, and injective modules, The dimension vector of a module and the Euler characteristic
Week 9Irreducible morphisms and almost split sequences
Week 10The Auslander-Reiten translations
Week 11Midterm exam
Week 12The Auslander-Reiten translations, The first Brauer-Thrall conjecture
Week 13The first Brauer-Thrall conjecture
Week 14Functorial approach to almost split sequences
Week 15Preparation for final exam
Week 16Final Exam

Assesment methods

Course activitiesNumberPercentage
Attendance00
Laboratory00
Application00
Field activities00
Specific practical training00
Assignments525
Presentation00
Project00
Seminar00
Midterms225
Final exam150
Total100
Percentage of semester activities contributing grade succes750
Percentage of final exam contributing grade succes150
Total100

WORKLOAD AND ECTS CALCULATION

Activities Number Duration (hour) Total Work Load
Course Duration (x14) 14 3 42
Laboratory 0 0 0
Application000
Specific practical training000
Field activities000
Study Hours Out of Class (Preliminary work, reinforcement, ect)1415210
Presentation / Seminar Preparation000
Project000
Homework assignment51470
Midterms (Study duration)21224
Final Exam (Study duration) 11414
Total Workload3658360

Matrix Of The Course Learning Outcomes Versus Program Outcomes

D.9. Key Learning OutcomesContrubition level*
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*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest