Editing Projective linear group (section)

=== Covering groups ===
Over the real and complex numbers, the projective special linear groups are the ''minimal'' ([[centerless]]) [[Lie group]] realizations for the special linear Lie algebra <math>\mathfrak{sl}(n)\colon</math> every connected Lie group whose Lie algebra is <math>\mathfrak{sl}(n)</math> is a cover of {{nowrap|PSL(''n'', ''F'')}}. Conversely, its [[universal covering group]] is the ''maximal'' ([[simply connected]]) element, and the intermediary realizations form a [[Covering group#Lattice of covering groups|lattice of covering groups]].

For example, [[SL2(R)|{{nowrap|SL(2, '''R''')}}]] has center {{mset|±1}} and fundamental group '''Z''', and thus has universal cover {{nowrap|{{overline|SL(2, '''R''')}}}} and covers the centerless {{nowrap|PSL(2, '''R''')}}.