Teoria de Lie

Code:

M4159

Acronym:

M4159

Level:

400

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:M	15	Official study plan since 2024/2025	1	-	6	42	162
			2

Teaching language

Portuguese

Objectives

To introduce students to the bases of Lie groups and Lie algebras.

Learning outcomes and competences

To understand the correspondence between Lie groups and Lie algebras and to use it to study Lie group representations.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Linear Algebra and Differential Geometry.

Program

Topological groups. Covering spaces. Lie groups and Lie algebras. Representaions of Lie algebras and of Lie groups.

Mandatory literature

José Carlos Santos; Grupos e álgebras de Lie, IST Press, 2011. ISBN: 978-989-8481-04-7

Teaching methods and learning activities

In-person teaching, with exercise resolutions.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	50,00
Teste	50,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	120,00
Frequência das aulas	42,00
Total:	162,00

Eligibility for exams

There is no record of absences. So, going to classes is not required to obtain attendance.

Calculation formula of final grade

The final classification will be the sum of the classifications obtained in the test (1st part of the syllabus) and in the exam in the normal season (2nd part of the syllabus). The exam at the appeal period will cover the entire syllabus.