Dyson’s classification and real division superalgebras

Roman Geiko, Gregory W. Moore

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number299
JournalJournal of High Energy Physics
Issue number4
StatePublished - Apr 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • Global Symmetries
  • Space-Time Symmetries


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