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ALGEBRA SUPERIORE B

Degree course: 
Corso di Second cycle degree in MATHEMATICS
Academic year when starting the degree: 
2016/2017
Year: 
1
Academic year in which the course will be held: 
2016/2017
Course type: 
Compulsory subjects, characteristic of the class
Credits: 
8
Period: 
Second semester
Standard lectures hours: 
80
Detail of lecture’s hours: 
Lesson (80 hours)
Requirements: 

Knowledge of basic algebraic structures and their properties: groups, rings, polynomials, fields. Knowledge of basic results in linear algebra and matrix calculus.

Final Examination: 
Orale
Assessment: 
Voto Finale

Teaching objectives and expected learning outcomes
Knowledge of main results in representation theory of finite groups.

Course program
Introduction of representation and equivalent notions: group algebras and modules.

Decomposition of modules as sums of irreducible modules: Mashke's theorem.

Character of a representation: inner product of characters and ortogonality relations. Character tables.
Induced character and Frobenius' reciprocity.
Applications to finite groups: Burnside's theorem.

Type of didactic activities
Frontal lectures and guided exercises.

Texts and teaching material

I. Isaacs, Character Theory of finite Groups, Dover

J. L. Alperin, R. Bell, Groups and Representations, Springer

G. James, M. Liebeck, Representations and Character of Groups, Cambridge University Press

For further detail go to the web page

Verification of learning skills
Written examination immediately followed by an oral examination.

Professors

MONTI VALERIO

Borrowers