Module Details |
| The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module. |
| Title | REPRESENTATION THEORY OF FINITE GROUPS | ||
| Code | MATH442 | ||
| Coordinator |
Dr A Rizzardo Mathematical Sciences Alice.Rizzardo@liverpool.ac.uk |
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| Year | CATS Level | Semester | CATS Value |
| Session 2023-24 | Level 7 FHEQ | First Semester | 15 |
Aims |
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Representation theory is one of the standard tools used in the investigation of finite groups, especially via the character of a representation. This module will be an introduction to these ideas with emphasis of the calculation of character tables for specific groups. |
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Learning Outcomes |
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(LO1) To use representation theory as a tool to understand finite groups. |
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(LO2) To be able to calculate character tables of a variety of groups. |
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(S1) Problem solving skills |
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(S2) Numeracy |
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Syllabus |
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Representations, examples, G-modules and Maschke's theorem, Schur's lemma. Character theory: inner products, decompositions of the group algebra, orthogonality relations. Calculation of character tables using commutator subgroup, inflation and induction. Application in quantum chemistry. |
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Recommended Texts |
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| Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module. | |
Pre-requisites before taking this module (other modules and/or general educational/academic requirements): |
| MATH244 Linear Algebra and Geometry |
Co-requisite modules: |
Modules for which this module is a pre-requisite: |
Programme(s) (including Year of Study) to which this module is available on a required basis: |
Programme(s) (including Year of Study) to which this module is available on an optional basis: |
Assessment |
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| EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
| Final Assessment | 120 | 70 | ||||
| CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
| Homework 1 | 0 | 10 | ||||
| Homework 2 | 0 | 10 | ||||
| Homework 3 | 0 | 10 | ||||