Dyson’s classification and real division superalgebras

TY - JOUR

T1 - Dyson’s classification and real division superalgebras

AU - Geiko, Roman

AU - Moore, Gregory W.

N1 - Publisher Copyright: © 2021, The Author(s).

PY - 2021/4

Y1 - 2021/4

N2 - 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.

AB - 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.

KW - Global Symmetries

KW - Space-Time Symmetries

UR - http://www.scopus.com/inward/record.url?scp=85105239930&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85105239930&partnerID=8YFLogxK

U2 - 10.1007/JHEP04(2021)299

DO - 10.1007/JHEP04(2021)299

M3 - Article

SN - 1126-6708

VL - 2021

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 4

M1 - 299

ER -