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Course Description Course Name : Lie Algebras I Course Code : MT-527 Course Type : Optional Level of Course : Second Cycle Year of Study : 1 Course Semester : Fall (16 Weeks) ECTS : 6 Name of Lecturer(s) : Prof.Dr. NAİME EKİCİ Asst.Prof.Dr. ZEYNEP YAPTI ÖZKURT Learning Outcomes of the Course : learns the existence of non associative algebras classifies low dimensional Lie algebras Using nilpotent, solvable and simple Lie algebras classifies finite dimensional complex Lie algebras Learns the Engel´ s and Lie´ s theorems and their applications Solves some problem using Lie algebra representations Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : 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 Contents : Lie algebras, subalgebras, ideals, homomorphisms, fundamental theorems, modules, Schur´ s Lemma Language of Instruction : Turkish Work Place : Classroom   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Definition of Lie algebras , examples, subalgebras, ideals Study the relevant sections in the book Lecture 2 Homomorphisms, structure constants Study the relevant sections in the book Lecture 3 The relationship between quotient algebras and ideals Study the relevant sections in the book Lecture 4 Classification of low dimensional Lie algebras Study the relevant sections in the book Lecture 5 Solvable and nilpotent Lie algebras Study the relevant sections in the book Lecture 6 Nilpotent transformations and the invariance lemma Study the relevant sections in the book Lecture 7 Applications of the invariance lemma Study the relevant sections in the book Lecture 8 Midterm exam Review and Problem Solving Written exam 9 Proofs of Engel´s and Lie´s Theorems Study the relevant sections in the book Lecture 10 Lie algebra representations and examples Study the relevant sections in the book Lecture 11 Modules over Lie algebras Study the relevant sections in the book Lecture 12 Submodules and quotient modules Study the relevant sections in the book Lecture 13 Irreducible and indecomposable modules Study the relevant sections in the book Lecture 14 Schur´s Lemma Study the relevant sections in the book Lecture 15 Exercises Solving relevant problems in the book Problem Solving 16/17 Final exam Review and Problem Solving Written examination   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Introduction to Lie Algebras (Karin Erdmann, Mark J. Wildon),  Lie Algebras (N. Jacobson)  Lie Algebras Part 1 (G.G.A. Bauerle, E.A. De Kerf) Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 80     Homeworks/Projects/Others 10 20 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Aquires sufficient knowledge to enable one to do research over and above the undergraduate level 5 2 Learns theoretical foundations of his/her field thoroughly 5 3 Uses the knowledge in his/her field to solve mathematical problems 3 4 Proves basic theorems in different areas of Mathematics 4 5 Creates a model for the problems in his/her field and expresses the relationship between objects in a simple and comprehensive way. 2 6 Uses technical tools in his/her field 5 7 Works independently in his/her field requiring expertise 5 8 Works with other colleagues collaboratelly, takes responsibilities if necessary during the research process 2 9 Argues and analyzes knowledge in his/her field and applies them in other fields if necessary 4 10 Has sufficient knowledge to follow literature in his/her field and communicate with stakeholders 3 11 Uses the language and technology to develop knowledge in his/her field and shares these with stakeholders systematically when necessary 4 12 Knows and abides by the ethical rules in analyzing, solving problems and publishing results 1 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 3 42     Out of Class Study (Preliminary Work, Practice) 14 3 42 Assesment Related Works     Homeworks, Projects, Others 10 3 30     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 15 15 Total Workload: 144 Total Workload / 25 (h): 5.76 ECTS Credit: 6