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# Algebraic Groups - MAT00003M

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• Department: Mathematics
• Module co-ordinator: Dr. Haralampos Geranios
• Credit value: 10 credits
• Credit level: M
• Academic year of delivery: 2020-21

## Related modules

• None

### Prohibited combinations

• None

Pre-requisite knowledge for MSc students: A second course on Group Theory; a course on Algebraic Geometry.

## Module will run

Occurrence Teaching cycle
A Spring Term 2020-21

## Module aims

The aims of the module are to: introduce the notion of an algebraic group as a group which also carries the structure of an affine variety; to study particular algebraic groups such as special linear groups, also solvable algebraic groups, connected algebraic groups and tori; to develop some of the general properties of these groups via a small amount of representation theory.

## Module learning outcomes

• The concept of an algebraic group as a group and an affine variety or algebraic set in affine space.

• How the group operations viewed as homomorphisms of algebraic sets influence the group structure of an algebraic group.

• Common examples of groups, such as general linear groups, special linear groups and groups of upper triangular matrices in the context of algebraic group theory.

• The notion of the connected component of an algebraic group and be able to compute it in simple examples.

• Diagonalisable groups.

## Module content

Syllabus:

• The definition of a linear algebraic group, homomorphisms, classical examples.
• The linearization procedure.
• The character group and diagonalizable groups.
• The identity component.

## Assessment

Task Length % of module mark
Online Exam - 24 hrs (Centrally scheduled)
Algebraic Groups
N/A 100

None

### Reassessment

Task Length % of module mark
Online Exam - 24 hrs (Centrally scheduled)
Algebraic Groups
N/A 100

## Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.