Majorana Algebra for the Hoffman-Singleton Graph
Andries E. Brouwer, Alexander A. Ivanov
TL;DR
This paper explores the application of Majorana algebra theory to the Hoffman-Singleton graph, focusing on the unique Majorana representation of the group U3(5) within the Monster group, and computes its dimension.
Contribution
It establishes the uniqueness of the Majorana representation of U3(5) in the Monster and calculates its dimension as 798.
Findings
Proved the uniqueness of the Majorana representation of U3(5).
Calculated the dimension of this representation as 798.
Connected the algebraic structure to the Hoffman-Singleton graph.
Abstract
Majorana theory is an axiomatic tool introduced by A. A. Ivanov in 2009 for studying the Monster group M and its subgroups through the 196884-dimensional Conway-Griess-Norton algebra. The group U3(5) is the socle of the centralizer in M of a subgroup of order 25. The involutions of this U3(5)-subgroup are 2A-involutions in the Monster. Therefore, U3(5) possesses a Majorana representation based on the embedding in the Monster. We prove that this is the unique Majorana representation of U3(5), and calculate its dimension, which is 798.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Finite Group Theory Research