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Level: MSci, MSc
Title: Reflection groups and coxeter groups
Supervisor:

Dr Matt Fayers
Research Area: Algebra
Description:

A reflection group is a subgroup of the group of symmetries of Euclidean space which is generated by the reflections it contains. Reflection groups have applications to Lie algebras and regular polytopes, but are interesting in their own right. The finite reflection groups have been classified, and remarkably can be characterised as the finite groups with a presentation of a particular kind: the Coxeter groups. The project would give an account of some parts of the book by Humphreys, before perhaps moving on to more specialised topics.
Further Reading:
  • J. Humphreys, Reflection groups and Coxeter groups. Cambridge Univ. Press, 1990.
Key Modules:

MTH6104 Algebraic Structures II (essential)

MTH5100 Algebraic Structures I (desirable)

MTH4103 Geometry I

MTH5112 Linear Algebra I
Other Information:
Current Availability: Yes