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Università degli Studi di Parma Università degli Studi di Parma
University of Parma
Course catalogue
Università degli Studi di Parma
course catalogue

GROUP THEORY
cod. 01096

Academic year 2009/10
3° year of course - First semester
Professor
Academic discipline
Geometria (MAT/03)
Field
Interdisciplinarità e applicazioni
Type of training activity
Related/supplementary
32 hours
of face-to-face activities
4 credits
hub:
course unit
in - - -
lectures timetable unavailable
exam calls
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Learning objectives

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The course aims to provide basic knowledge of the theory of finite groups and classical matrix groups.

Prerequisites

Basic knowledge of Linear Algebra.

Course unit content

<br />Definition of group and subgroup. Right and left laterals. Lagrange's theorem and its consequences. Normal subgroups. Quotient group. Homomorphisms between groups. Homomorphism theorems. Sylow's theorem and its applications. <br />
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Classical matrix groups: linear, orthogonal and unitary groups. <br />
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Group parameters and canonical parameters: continuous groups. <br />
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Definition of exponential of a matrix and of logarithm of a matrix. Notion of Lie group of matrices and associated Lie Algebra. <br />
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J-orthogonal group: simplectic group. Lorentz group and Poincare group. <br />
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Outline of topology and topological properties of classical matrix groups. Subgroups to a parameter. Matrix groups as variety. Vector space tangent to identity. 

Full programme

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Bibliography

M.L. Curtis, Matrix Groups, Springer-Verlag

Teaching methods

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Assessment methods and criteria

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Other information

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