Group Theory I
General data
Course ID: | 1100-3`TG1 |
Erasmus code / ISCED: |
11.102
|
Course title: | Group Theory I |
Name in Polish: | Teoria grup I |
Organizational unit: | Faculty of Physics |
Course groups: |
Astronomy, individual path; elective courses Physics (2nd cycle); courses from list "Selected Problems of Modern Physics" Physics, individual path; elective courses |
ECTS credit allocation (and other scores): |
6.00
|
Language: | Polish |
Prerequisites (description): | Analysis and algebra |
Mode: | Classroom |
Short description: |
The course is devoted to basic group theory, representations of groups, theory of Lie groups and algebras. It will discuss some applications of groups to physics |
Full description: |
The course will present basic concepts of group theory ant theory of group representations as well as more advanced topics directed towards applications in physics. Covered material will also serve as basis for more advanced topics offered in the spring semester. Program: 1. Basics of group theory (group, subgroup, homomorphism, normal subgroup, quotient space and quotient group, product of groups, semidirect product of groups, group actions, homogeneous spaces, group algebra) 2. Representations of finite and compact groups (representation, subrepresentation, irreducible representation, Peter-Weyl theorem, character of a representation, finding all irreducible representations, decomposition of the group algebra, example: representations of the symmetric group, extension to compact groups) 3. Commutative groups, Pontriagin duality (Rn and Zn) (dual group of a commutative group, Fourier transformation) 4. Induced representations (induced representation, elements of Mackey's theory of representations of semidirect product of a commutative group, example: Poincare group) 5. Lie groups and Lie algebras (Lie group, Lie algebra of a Lie group, examples: classical matrix groups: GL(n), SU(n), SO(n), SL(n,C), morphisms of Lie groups and Lie algebras, adjoint representation, exponential map, Maurer-Cartan form) Student's effort Lectures: 30 h -- 1 ECTS Exercise classes: 30 h -- 1 ECTS Preparation for the lectures and classes: 30 h -- 1 ECTS Homework problems and preparation for the test: 30 h - 1 ECTS Preparation for the exam: 30 h -- 1 ECTS |
Bibliography: |
1. A. Trautman "Grupy oraz ich reprezentacje" (lecture notes WF UW) 2. J.P. Serre "Reprezentacje liniowe grup skończonych" 3. A. Barut, R. Rączka "Theory of group representations and applications" 4. B.Simon, "Representations of finite and compact groups" |
Learning outcomes: |
Knowledge: Familiarity with basic group theory and theory of group representations. Skills: Ability to solve simple problems of group theory and the theory of group representations, in particular involving the semisimple product, characters of representations, decomposition into irreducible components for finite groups Attitude: Appreciation of the beauty, depth and importance of group theory, especially in the context of its applications in physics. |
Assessment methods and assessment criteria: |
Every student has to get a positive grade based on the performance at exercise classes and pass the written and oral exams. |
Practical placement: |
Does not apply |
Classes in period "Winter semester 2023/24" (past)
Time span: | 2023-10-01 - 2024-01-28 |
Navigate to timetable
MO CW
TU W TH FR WYK
|
Type of class: |
Classes, 30 hours, 30 places
Lecture, 30 hours, 30 places
|
|
Coordinators: | Rafał Suszek | |
Group instructors: | Szymon Charzyński, Rafał Suszek | |
Students list: | (inaccessible to you) | |
Examination: |
Course -
Examination
Lecture - Examination |
Classes in period "Winter semester 2024/25" (future)
Time span: | 2024-10-01 - 2025-01-26 |
Navigate to timetable
MO CW
TU W TH FR WYK
|
Type of class: |
Classes, 30 hours, 30 places
Lecture, 30 hours, 30 places
|
|
Coordinators: | Rafał Suszek | |
Group instructors: | Szymon Charzyński, Rafał Suszek | |
Students list: | (inaccessible to you) | |
Examination: |
Course -
Examination
Lecture - Examination |
Copyright by University of Warsaw.