TÜRKÇE
ENGLISH
Information
| Code | MT569 |
| Name | Topics in Lie Algebras |
| 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 | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ZERRİN GÜL ESMERLİGİL |
Course Goal / Objective
The aim of this course is to enable students to learn Lie algebras and their applications that provide identity relations.
Course Content
Rings, Modules, Algebras, Semi-Product Multiplication, Direct Total, Ideals Series, Lie algebra on modules, semisimple series, Nilpotent Lie algebras, Soluble Lie algebras, Free algebra, Free Lie algebra
Course Precondition
Yok
Resources
Lie Algebras Theory And Algorithms Willem A. de Graaf
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learn to explain the theory of Lie algebras in a modern way. |
| LO02 | Learns the existence of Lie algebras which have a relation of identity. |
| LO03 | Perform the Lie algebras which have a relation of identity. |
| LO04 | Knows the structure of algebras on the unit elements and commutative rings. |
| LO05 | Learn the proof techniques of some important results by using series of ideals in Lie algebras. |
| LO06 | Understands the concept of freedom, basics of free Lie algebras. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows the results of previous research in a special field of mathematics | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 5 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics | 5 |
| 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. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics | 5 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Sets up original problems in her field and offers different solution techniques | |
| PLO08 | Bilgi - Kuramsal, Olgusal | It carries out original and qualified scientific studies on the subject related to its field. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | 4 |
| 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. | 3 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have foreign language knowledge at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | 5 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | It 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 | Rings, Moduls, Fields | Lecture Discussion | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Semidirect multiplies, Direct sums, ideal series | Lecture Discussion | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Moduls, Modul on Lie algebras,semibasic series | Lecture Discussion | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Nilpotent Lie algebras, Frattini subalgebras, endomorfizm of Nilpotent Lie algebras | Lecture Discussion | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Solvable Lie algebras, Engel Lie algebras | Lecture Discussion | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Frattini Teory for Lie algebras, Graded algebras | Lecture Discussion | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Homogen subalgebras, Restricted Lie algebras | Lecture Discussion | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Lecture Discussion | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Free groupoid | Lecture Discussion | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Free algebras,Free Lie algebras | Lecture Discussion | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Free asosociative algebras, | Lecture Discussion | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Basis of Free Lie algebras | Lecture Discussion | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Subalgebras of Free Lie algebras | Lecture Discussion | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Free generators, Universal enveloping algebras and Poincare- Birkhof- Witt Theorems | Lecture Discussion | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Free Decomposition | Lecture Discussion | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | Lecture Discussion | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Lecture Discussion | 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 | ||