Course Name Code Semester T+U Hours Credit ECTS
Lie Groups and Lie Algebras II MAT 591 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Doç.Dr. MAHMUT AKYİĞİT
Course Lecturers
Course Assistants
Course Category
Course Objective The lie groups and lie algebras II course aims to give the fundamental knowledge for the studies of graduate students who study at topology, algebra and geometry branch.
Course Content sl(2) and its Representations, The Lie algebra of an algebraic group, Reel and Complex Lie groups and Algebras, Split Complex and Dual Lie Groups, Topology of Lie Groups, Compact Lie groups, Compactness , Connectedness, The maximal torus of a compact Lie group, Nillpotent Lie Groups, Matrix groups and transformation groups, Dynkin Diagrams Cartan Matrices, Classification of Dynkin diagrams, Casimir elements and Weyl teorems, Simple roots, Properties of root systems, Actions of Lie groups and Lie algebras
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/She realizes the lie algebra of an algebraic group Lecture, Question-Answer, Discussion, Brain Storming, Self Study, Problem Solving, Testing, Homework,
2 He/She learns split complex and dual lie groups Lecture, Question-Answer, Discussion, Brain Storming, Self Study, Problem Solving, Testing, Homework,
3 He/She realizes nillpotent lie groups Lecture, Question-Answer, Discussion, Brain Storming, Self Study, Problem Solving, Testing, Homework,
4 He/She realizes Dynkin diagrams cartan matrices Lecture, Question-Answer, Discussion, Brain Storming, Self Study, Problem Solving, Testing, Homework,
5 He/She learns actions of lie groups and lie algebras Lecture, Question-Answer, Discussion, Brain Storming, Self Study, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 sl(2) and its Representations
2 The Lie algebra of an algebraic group
3 Reel and Complex Lie groups and Algebras
4 Split Complex and Dual Lie Groups
5 Topology of Lie Groups
6 Compact Lie groups, Compactness , Connectedness
7 The maximal torus of a compact Lie group
8 Nillpotent Lie Groups
9 Matrix groups and transformation groups
10 Dynkin Diagrams Cartan Matrices
11 Classification of Dynkin diagrams
12 Casimir elements and Weyl teorems
13 Simple roots, Properties of root systems
14 Actions of Lie groups and Lie algebras
Resources
Course Notes 1.) Lie Groups, Lie Algebras and Representation Theory: An Introduction, Brian C. Hall, (2005) Graduate Texts in Mathematics, Springer Verlag<br>2.) Lie Groups: An Introduction through Linear Groups, W. Rossman, (2005) Oxford Graduate Texts in Mathematics, Oxford Science Publications
Course Resources
Order Program Outcomes Level of Contribution
1 2 3 4 5
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Kısa Sınav 10
1. Ödev 10
2. Ödev 10
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 10 10
Quiz 1 10 10
Assignment 2 16 32
Final examination 1 10 10
Total Workload 158
Total Workload / 25 (Hours) 6.32
dersAKTSKredisi 6