A construction for a central
extension of a group satisfying a certain set of axioms has been given by C. W.
Curtis. These groups are called groups of Lie type. The construction is based on
that given by R. Steinberg for covering groups of the Chevalley groups. The
central extensions constructed by Curtis, however, are not covering groups in
the sense of being universal central extensions, as he shows by an example.
Here, the Steinberg construction is considered for a more restricted class of
groups of Lie type. It is shown that in this case, the central extension is
a covering. It is also shown that this more restricted definition of groups
of Lie type still includes the Chevalley and twisted groups, with certain
exceptions.
