This module is not currently running in 2024 to 2025.
Roughly speaking, a diagram algebra has a basis consisting of some sort of diagrams and a multiplication coming from concatenation of diagrams. There is no formal definition, just a host of interesting algebras arising in different parts of mathematics and physics (for example the invariant theory of classical groups, algebraic Lie theory, knot theory, integrable models and statistical mechanics, quantum computing). Outline syllabus: associative algebras and an introduction to representation theory; examples of diagram algebras; an introduction to statistical mechanics; diagram algebras in mathematical physics.
24 hours if lectured. The module may be offered as a directed reading course.
80% Examination, 20% Coursework
We will not follow a single text, but will provide course materials.
C.W.Curtis and I. Reiner, Representation Theory of Finite Groups and Associate Algebras, Interscience (1962). (B)
S.Koenig, A panorama of diagram algebras. Trends in representation theory of algebras and related topics, 491-540, EMS Ser. Congr. Rep., Eur. Math. Soc., Zurich, 2008. (B)
P. Martin, Potts models and related problems in statistical mechanics. Series on Advances in Statistical Mechanics, vol. 5, World Scientific Publishing Co. Inc., Teaneck NJ, 1991. (B)
A. Doikou, S. Evangelisti, G. Feverati, N. Karaiskos, Introduction to Quantum Integrability, Int. J. Mod. Phys. A25:3307-3351 2010. (B)
See the library reading list for this module (Canterbury)
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