MT527 Lie Algebras I

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

Information

Code MT527
Name Lie Algebras I
Term 2024-2025 Academic Year
Semester . Semester
Duration (T+A) 3-0 (T-A) (17 Week)
ECTS 6 ECTS
National Credit 3 National Credit
Teaching Language Türkçe
Level Yüksek Lisans Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Doç. Dr. ZEYNEP ÖZKURT


Course Goal / Objective

The aim of this course is to introduce Lie algebras and to acquaint the students with non associative algebras by teaching the basic algebraic notions of Lie algebras

Course Content

Lie algebras, subalgebras, ideals, homomorphisms, fundamental theorems, modules, Schurs Lemma

Course Precondition

no

Resources

Karin Erdman, Mark Wildon Introduction to Lie Algebras

Notes

Jacobson, Lie Algebras


Course Learning Outcomes

Order Course Learning Outcomes
LO01 learns the existence of non associative algebras
LO02 classifies low dimensional Lie algebras
LO03 Using nilpotent, solvable and simple Lie algebras classifies finite dimensional complex Lie algebras
LO04 Learns the Engels theorems and their applications
LO05 Solves some problem using Lie algebra representations


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. 4
PLO02 Bilgi - Kuramsal, Olgusal Knows in detail the relationship between the results in his area of ​​expertise and other areas of mathematics. 4
PLO03 Bilgi - Kuramsal, Olgusal Establishes new mathematical models with the help of the knowledge gained in the field of specialization.
PLO04 Bilgi - Kuramsal, Olgusal Has basic knowledge in all areas of mathematics.
PLO05 Bilgi - Kuramsal, Olgusal It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. 4
PLO06 Bilgi - Kuramsal, Olgusal Effectively uses the technical equipment needed to express mathematics.
PLO07 Bilgi - Kuramsal, Olgusal poses original problems related to field and presents different solution techniques. 4
PLO08 Bilgi - Kuramsal, Olgusal carries out original and qualified scientific studies on the subject related to its field. 4
PLO09 Bilgi - Kuramsal, Olgusal Analyzes existing mathematical theories and develops new theories. 3
PLO10 Beceriler - Bilişsel, Uygulamalı Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education.
PLO11 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. 3
PLO12 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. 3
PLO13 Yetkinlikler - Öğrenme Yetkinliği Adheres to the ethical rules required by its scientific title 5


Week Plan

Week Topic Preparation Methods
1 Definition of Lie algebras , examples, subalgebras, ideals Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
2 Homomorphisms, structure constants Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
3 The relationship between quotient algebras and ideals Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
4 the book Lecture 4 Classification of low dimensional Lie algebras Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
5 Solvable and nilpotent Lie algebras Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
6 Nilpotent transformations and the invariance lemma Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
7 Applications of the invariance lemma Study the relevant sections in the book Ölçme Yöntemleri:
Yazılı Sınav
8 Mid-Term Exam Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
9 Proofs of Engels Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
10 Lie algebra representations and examples Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
11 Modules over Lie algebras Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
12 Submodules and quotient modules Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
13 Irreducible and indecomposable modules Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
14 Schurs Lemma Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
15 Exercises Study the relevant sections in the book Öğretim Yöntemleri:
Anlatım
16 Term Exams Study the relevant sections in the book Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Study the relevant sections in the book Ölçme Yöntemleri:
Yazılı Sınav


Student Workload - ECTS

Works Number Time (Hour) Workload (Hour)
Course Related Works
Class Time (Exam weeks are excluded) 14 3 42
Out of Class Study (Preliminary Work, Practice) 14 5 70
Assesment Related Works
Homeworks, Projects, Others 0 0 0
Mid-term Exams (Written, Oral, etc.) 1 15 15
Final Exam 1 30 30
Total Workload (Hour) 157
Total Workload / 25 (h) 6,28
ECTS 6 ECTS

Update Time: 09.05.2024 11:37