MT569 Topics in Lie Algebras

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

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

Update Time: 09.05.2024 11:39