An Introduction to Majorana Theory

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• Madeleine Whybrow, Imperial College London
• Friday 15 January 2016, 15:00-16:00
• CMS, MR4.

If you have a question about this talk, please contact Nicolas Dupré.

Majorana theory was introduced in 2009 by A.A. Ivanov as an axiomatisation of certain properties of the Monster group $\mathbb{M}$ and the Greiss Algebra $V_{\mathbb{M}}$. The main aim of Majorana theory is to describe the subalgebra structure of $V_{\mathbb{M}}$. Ivanov’s work was inspired by a result of S. Sakuma who classified certain subalgebras of $V_{\mathbb{M}}$ within the context of Vertex Operator Algebras (VOAs), objects which feature in the proof of Montrous Moonshine.

The crucial definition in Majorana theory is that of a Majorana algebra, a commutative real algebra generated by a set of idempotents which obeys certain axioms. Similarly, given a finite group $G$, it is possible to define a Majorana representation of $G$. In this talk, I will cover the basic ideas of Majorana theory before discussing my own work on the Majorana representations of certain groups of interest in the context of the Monster.

This talk is part of the Junior Algebra and Number Theory seminar series.

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