What is SU*(N)? Definition and Explanation

[William Nelso]

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).

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^-1X* 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)

 

[fresh_42]

The original paper is here:
https://cds.cern.ch/record/140183/files/198301032.pdfI guess the star indicates the projective group, that is the factor group of its center $\varepsilon_n \cdot \mathbb{1}$ with n-th roots of unity $\varepsilon_n$.