Groups and their representations

Recommended Prerequisites

Basic courses in Linear Algebra and Algebra, Commutative Algebra.

Teaching Methods

Classes are mainly expository and include examples and exercises to apply the material being taught. Students are given topics which should be worked at home and presented during classes.
Extensive tutorial time is offered to the students to clarify their difficulties with the theory and to help them with the homework assignments and preparation for the exams.

Learning Outcomes

The main goal of this curricular unit is to teach the students to work with groups and their representations and to encourage them to do research in this area.

Work Placement(s)

No

Syllabus

Symmetric, alternating and dihedral groups. Representations of algebras and groups; irreducible representations; semi-simple representations; Maschke’s Theorem. Tensor products of modules; induced representations. Character theory.

Head Lecturer(s)

Ana Paula Jacinto Santana Ramires

Assessment Methods

Continuous assessment
During the semester there is one mid-term exam (50-75% of the final grade) and the presentation during the classes of essays on topics given to each student individually (50-25% of the final grade): 100.0%

Final assessment
Exam: 100.0%

Bibliography

C.W. Curtis, I. Reiner, Methods of Representation Theory with Applications to Finite Groups and Orders, Vol I, Wiley-Interscience, 1990.

K. Erdman, Algebras, Mathematical Institute, University of Oxford, 2007.

 

G. James, M. Liebeck, Representations and Characters of Groups, Cambridge University Press, segunda edição, 2001.