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Keywords:
Categorical groups; stable 3-stem; categorified super-symmetry; ADE classification; Schur theory; platonic solids
Categorical groups; stable 3-stem; categorified super-symmetry; ADE classification; Schur theory; platonic solids
Summary:
We recall Schur’s work on universal central extensions and develop the analogous theory for categorical extensions of groups. We prove that the String 2-groups are universal in this sense and proceed study their restrictions to the finite subgroups of the 3-sphere $\it Spin(3)$ and to the spin double covers of the alternating groups. We find that almost all of these restrictions are universal categorical extensions and that the categorical extensions of the alternating family are governed by the stable 3-stem $\pi_3(\Bbb S^0)$.
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