Abstract
It is well-known that unitary irreducible representations of groups can be usefully classified in a 3-fold classification scheme: Real, Complex, Quaternionic. In 1962 Freeman Dyson pointed out that there is an analogous 10-fold classification of irreducible representations of groups involving both unitary and antiunitary operators. More recently, it was realized that there is also a 10-fold classification scheme involving superdivision algebras. Here we give a careful proof of the equivalence of these two 10-fold ways.
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ArXiv ePrint: 2010.01675
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Geiko, R., Moore, G.W. Dyson’s classification and real division superalgebras. J. High Energ. Phys. 2021, 299 (2021). https://doi.org/10.1007/JHEP04(2021)299
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DOI: https://doi.org/10.1007/JHEP04(2021)299