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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 | ||