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homotopy hypothesis-theorem
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A Platonic 2-group (Epa 10) is a 2-group higher extension of a “Platonic group” in the ADE classification, i.e. of a finite subgroup of SO(3); or else of its double cover, hence of finite subgroup of SU(2).
ADE classification and McKay correspondence
The universal Platonic 2-group extensions of finite subgroups of SU(2) by (Epa-Ganter 16, def.2.11) are equivalently the restrictions of the string 2-group extension of , hence the classifying cocycle is the restriction of the smooth second Chern class:
where is the canonical inclusion of roots of unity, .
See also at finite subgroup of SU(2) – Discrete torsion
Narthana Epa, Platonic 2-groups, 2010 (pdf)
Narthana Epa, Nora Ganter, Platonic and alternating 2-groups, Higher Structures 1(1):122-146, 2017 (arXiv:1605.09192, hs:30)
In relation to the Monster group:
Nora Ganter, Subtle Symmetries and the Refined Monster, project description (2018) [pdf, pdf]
Nora Ganter, Looking for a Refined Monster [arXiv:2405.16410]
Last revised on July 1, 2024 at 21:15:25. See the history of this page for a list of all contributions to it.