Course title  Introduction to the Theory of Lie Groups 

Course code  MU/03262 
Organizational form of instruction  Lecture + Lesson 
Level of course  Master 
Year of study  not specified 
Semester  Summer 
Number of ECTS credits  6 
Language of instruction  Czech 
Status of course  Compulsoryoptional 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Course availability  The course is available to visiting students 
Lecturer(s) 


Course content 
 The concept of a Lie group. Analytical, continuous and smooth groups. Hilbert's fifth problem.  Local theory of Lie groups.  Lie algebras. Tangent Lie algebra of a Lie group. Classification of simple Lie algebras.  General linear group and its subgroups. Linear representations. The Ado theorem.  The BakerCampbellHausdorff formula.  Differential geometry of Lie groups. Left and rightinvariant vector fields and differential forms. Onedimensional Lie subgroups. Solution of the MaurerCartan equations. Exponential map.  The global theory of Lie groups. The Cartan theorem. Construction of all Lie groups for a given tangent Lie algebra. Lie groups which have no faithful linear representations.  Transformation groups of manifolds and their actions. The fundamental vector fields. Principal bundles.

Learning activities and teaching methods 
unspecified 
Recommended literature 

Study plans that include the course 
Faculty  Study plan (Version)  Branch of study Category  Recommended year of study  Recommended semester 

Mathematical Institute in Opava  Mathematical Analysis (1IVT)  Mathematics courses  4  Summer 
Mathematical Institute in Opava  Mathematical Analysis (1)  Mathematics courses  1  Summer 