TOPICS IN ADVANCED ALGEBRA
Knowledge of basic algebraic structures and their properties: groups, rings, polynomials, fields. Knowledge of basic results in linear algebra and matrix calculus.
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
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Verification of learning skills
Written examination immediately followed by an oral examination.
Borrowed from
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