Information Package / Course Catalogue
Lie Algebra
Course Code: MTK622
Course Type: Area Elective
Couse Group: Third Cycle (Doctorate Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 8
Objectives of the Course

In Group Theory, play very important role in the classification of simple groups.

Course Content

Lie Algebras, Derivative, soluble and nilpotent Lie algebras, Semisimple Lie Algebras, Root systems.

Name of Lecturer(s)
Learning Outcomes
1.Classification of Simple groups
2.Carry derivation in analysis to group theory
3.Give more information about groups
4.To be able to gain the skill of interpreting some interrelations among these concepts
5.To be able to use mathematical concepts in solving certain types of problems
Recommended or Required Reading
1.Introduction to Lie Algebras and Representation Theory .Springer Verlag, 1972.
2.Simple Groups Of Lie Type. John Wiley and Sons. 1972
Weekly Detailed Course Contents
Week 1 - Theoretical
Basic concepts: Definitions and first examples
Week 2 - Theoretical
Ideals and homomorphisms,
Week 3 - Theoretical
Soluble and nilpotent Lie algebras
Week 4 - Theoretical
Semisimple Lie Algebras: Theorems of Lie and Cartan
Week 5 - Theoretical
Killing form
Week 6 - Theoretical
Complete reducibility of representation
Week 7 - Theoretical
Representation of SL(2,F)
Week 8 - Theoretical
Root space and decompositons
Week 9 - Theoretical
Root systems: Axiomatics
Week 10 - Theoretical
Simple roots and Weyl group
Week 11 - Theoretical
Classification
Week 12 - Theoretical
Construction of root systems and automorphisms
Week 13 - Theoretical
Abstract theory of weights
Week 14 - Theoretical
Borel subalgebra
Assessment Methods and Criteria
Type of AssessmentCountPercent
Assignment1%5
Term Assignment1%5
Midterm Examination1%20
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140342
Assignment1066
Term Project1066
Individual Work140570
Midterm Examination130232
Final Examination142244
TOTAL WORKLOAD (hours)200
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
OÇ-1
3
3
4
3
4
4
2
4
3
2
4
OÇ-2
3
3
4
3
4
4
2
4
3
2
4
OÇ-3
4
4
4
4
4
4
3
4
3
3
4
OÇ-4
4
4
4
4
4
OÇ-5
4
4
4
4
Adnan Menderes University - Information Package / Course Catalogue
2026