I've run across a Lie group notation that I am unfamiliar with and having trouble googling (since google won't seem to search on * characters literally).(adsbygoogle = window.adsbygoogle || []).push({});

Does anyone know the definition of the "star groups" notated e.g. SU*(N), SO*(N) ??

The paper I am reading states for example that SO(5,1) is isomorphic to SU*(4).

(Ref Kugo+Townsend, Nuc. Phys. B221, p. 357, "Supersymmetry and the division algebras")

In fact it has a "definition" of these groups, however I am not able to understand it. It appears to say that

SU*(N) consists of elements X of SL(N,C) such that

X = B^{-1}X* B

where B is the spinor conjugation operator (and N is the dimension of a spinor rep of the SO(D,1) that the paper is talking about)

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# A Star groups SU*(N)

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