Lie Algebras (MAST90132)
Graduate courseworkPoints: 12.5On Campus (Parkville)
Overview
| Availability | Semester 1 |
|---|---|
| Fees | Look up fees |
The theory of Lie algebras is fundamental to the study of groups of continuous symmetries acting on vector spaces, with applications to diverse areas including geometry, number theory and the theory of differential equations. Moreover, since quantum mechanical systems are described by Hilbert spaces acted on by continuous symmetries, Lie algebras and their representations are also fundamental to modern mathematical physics. This subject develops the basic theory in a way accessible to both pure mathematics and mathematical physics students, with an emphasis on examples. The main theorems are: the classification of complex semi-simple Lie algebras in terms of Cartan matrices and Dynkin diagrams, and the classification of finite-dimensional representations of these algebras in terms of highest weight theory.
Intended learning outcomes
On completion of this subject, students should be able to demonstrate:
- An understanding of the abstract theory of Lie algebras, and how they arise from Lie groups;
- The ability to analyse examples of semisimple Lie algebras using the language of roots and coroots;
- An understanding of the abstract theory of representations of Lie algebras;
- The ability to analyse examples of representations using the language of weights; and
- Facility with some basic applications of this theory to the study of symmetries in physical systems.
Generic skills
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- Problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- Analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- Collaborative skills: the ability to work in a team; and
- Time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 5 April 2025
Eligibility and requirements
Prerequisites
One of
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST30005 | Algebra | Semester 1 (On Campus - Parkville) |
12.5 |
| MAST30031 | Methods of Mathematical Physics | Semester 2 (On Campus - Parkville) |
12.5 |
Corequisites
Non-allowed subjects
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 5 April 2025
Assessment
| Description | Timing | Percentage |
|---|---|---|
One written assignment
| Early in the teaching period | 10% |
One written assignment
| Mid semester | 15% |
One written assignment
| Late in the teaching period | 15% |
A written examination
| During the examination period | 60% |
Last updated: 5 April 2025
Dates & times
- Semester 1
Coordinator David Ridout Mode of delivery On Campus (Parkville) Contact hours 36 hours: 3 x one-hour interactive lectures weekly Total time commitment 170 hours Teaching period 3 March 2025 to 1 June 2025 Last self-enrol date 14 March 2025 Census date 31 March 2025 Last date to withdraw without fail 9 May 2025 Assessment period ends 27 June 2025 Semester 1 contact information
What do these dates mean
Visit this webpage to find out about these key dates, including how they impact on:
- Your tuition fees, academic transcript and statements.
- And for Commonwealth Supported students, your:
- Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.
Last updated: 5 April 2025
Further information
- Texts
- Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
- Available to Study Abroad and/or Study Exchange Students
Last updated: 5 April 2025