Lie Algebras (MAST90132)

Graduate courseworkPoints: 12.5Not available in 2020

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For information about the University’s phased return to campus and in-person activity in Winter and Semester 2, please refer to the on-campus subjects page.

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Overview

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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.
  • Facility with some basic applications of this theory to the study of symmetries in physical systems.

Generic skills

  • 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.
  • Time-management skills: the ability to meet regular deadlines while balancing competing commitments.

Last updated: 3 November 2022

Eligibility and requirements

Prerequisites

Code Name Teaching period Credit Points
MAST30021 Complex Analysis
Semester 1 (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
 12.5

Corequisites

None

Non-allowed subjects

None

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: 3 November 2022

Assessment

Due to the impact of COVID-19, assessment may differ from that published in the Handbook. Students are reminded to check the subject assessment requirements published in the subject outline on the LMS

DescriptionTimingPercentage

Up to 40 pages of assignments (4 assignments worth 10% each spread evenly)

  • 40 pages
Throughout the teaching period40%

A written examination

  • 3 hours
During the examination period60%

Last updated: 3 November 2022

Dates & times

Not available in 2020

Last updated: 3 November 2022

Further information

  • Texts

    Prescribed texts

    There are no specifically prescribed or recommended texts for this subject.

  • 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

    This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.

Last updated: 3 November 2022