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Axial algebras and groups of 3-transpositions

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  • Full or part time
    Prof S Shpectorov
  • Application Deadline
    Applications accepted all year round
  • Competition Funded PhD Project (Students Worldwide)
    Competition Funded PhD Project (Students Worldwide)

Project Description

Axial algebras are nonassociative commutative algebras generated by idempotents satisfying specific fusion rules. The motivation for this class of algebras came from Physics and from the mathematical theory of Vertex Operator Algebras. The prize example of axial algebras is the real 196884-dimensional Griess-Norton algebra for the Monster sporadic simple group. In general, axial algebras are often related to groups, and such algebras are the focus of this PhD project. Drawing inspiration from the class of the so-called Matsuo algebras for groups of 3-transpositions, we will try to develop further classes of algebras for these groups. The project may involve computer calculations (for example, in the computer algebra system GAP) and so some programming experience is a plus.

Funding Notes

This research project is one of a number of projects in the School of Mathematics. It is in competition for funding with one or more of our advertised PhD projects. Usually the project which receives the best applicant will be supported.

Normally scholarships are only available to UK or EU citizens. Other nationals who are normally resident in the UK or those who have been resident in the UK for a period of 3 years or more are also eligible.

All students with the correct qualifications and access to independent funding are also welcome to apply.

Related Subjects

How good is research at University of Birmingham in Mathematical Sciences?

FTE Category A staff submitted: 40.00

Research output data provided by the Research Excellence Framework (REF)

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