Mark Ronan's website
196,884 and the Monster
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The number 196,884 is the
dimension of the space in which Robert Griess constructed the Monster. This representation in 196,884 dimensions splits
into two: a trivial representation in 1 dimension, and an irreducible
representation in 196,883 dimensions. The reason Griess
chose 196,884 dimensions is that the Monster preserves a pleasing algebra
structure in a space of this dimension, and the main work in his construction
was to give the multiplication for this algebra, and show that it was
preserved by the Monster. This algebra is now called the Griess algebra. The number 196,884 is also the
first non-trivial coefficient in the j-function
in number theory, and this strange coincidence led to a connection between
the Monster and the j-function,
known as Moonshine. The story of these connections,
and the history leading up to them, is described in my book Symmetry and the Monster. |
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