19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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Majorana Representations

Presented by Ms. Sophie DECELLE
Type: Oral presentation
Track: Group Actions

Content

Majorana Theory, introduced by A. A. Ivanov, is an axiomatisation of the properties of the Monster algebra, $V_{\mathbb{M}}$. It attempts to classify and describe subalgebras of the Monster algebra using the subgroup structure of the Monster simple group $\mathbb{M}$. For each embedding of a group $G$ into $\mathbb{M}$ we can define a Majorana representation of $G$ which defines a subalgebra of $V_{\mathbb{M}}$, provided the embedding satisfies one particular condition. The Majorana representations of the groups $S_4$, $A_5$, $A_6$, $A_7$, and $L_{3}(2)$ have been classified and shown to define proper subalgebras of $V_{\mathbb{M}}$. Here we show that there is a unique Majorana representation of $L_{2}(11)$ defining a proper subalgebra of $V_{\mathbb{M}}$. Using the permutation action of $L_2(11)$ on its subgroups of order $2,3$ and $5$, and the $2-(11,5,2)$ biplane, we give a description of its algebra and inner products.

Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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