Majorana representation of A6 involving 3C-algebras
Tóm tắt
We study a possible Majorana representation
$${{\mathcal R}}$$
of the alternating group A6 of degree 6 such that for some involutions s and t in A6, generating a D6-subgroup, the corresponding Majorana axes a
s
and a
t
generate a subalgebra of type 3C. We show that there exists at most one such representation
$${{\mathcal R}}$$
and that its dimension is at most 70. The representation
$${{\mathcal R}}$$
does not correspond to a subalgebra in the Monster algebra generated by a subset of the Majorana axes canonically indexed by the involutions of an A6-subgroup in the Monster.
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