Kursens beskrivning

LEARNING OUTCOMES

After completing the course the participant is able to:

 - describe symmetries in scientific and engineering problems using groups and their representations

 - linearlize the treatment of continuous symmetries described by Lie groups using their Lie algebras

 - analyze continuous symmetries with highest weight representations of Lie groups and Lie algebras.

Credits: 5

Schedule: 26.02.2024 - 17.04.2024

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Kalle Kytölä

Contact information for the course (applies in this implementation):

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English

CONTENT, ASSESSMENT AND WORKLOAD

Content

• valid for whole curriculum period:

  Groups and their representations.

  Lie groups and their Lie algebras.

  Representations of semisimple Lie algebras.

Assessment Methods and Criteria

• valid for whole curriculum period:

  Weekly exercises and exam.

Workload

• valid for whole curriculum period:

  - 2 x 2h lectures / week

  - 1 x 2h exercises sessions / week

DETAILS

Study Material

• valid for whole curriculum period:

  lecture notes "Finite groups, Lie groups, Lie algebras, and representations" by Kalle Kytölä

  W. Fulton & J. Harris "Representation theory: A first course", Graduate Texts in Mathematics. Springer, 2004.

Substitutes for Courses

• valid for whole curriculum period:

  Substitutes for Courses

Prerequisites

• valid for whole curriculum period:

  Prerequisites

FURTHER INFORMATION

Further Information

• valid for whole curriculum period:

  Teaching Language : English

  Teaching Period : 2022-2023 No teaching
  2023-2024 Spring IV

  Enrollment :

  Registration takes place in Sisu (sisu.aalto.fi).

Beskrivning