Dirk Mittenhuber:
A globality theorem for wedges that are bounded by a hyperplane ideal
Journal of Lie Theory, vol. 2 (2), p. 213-221
We consider a Lie group $G$ containing a normal subgroup $N\unlhd G$
such that $G/N\cong\reals$, i.e the Lie algebra $\n$
is a hyperplane ideal in $\g$.
A natural question that arises in this context is the following: Suppose we
are given a Lie-wedge $W$ which is contained in a halfspace bounded by
$\n$.
Under which conditions is $W$ global in $G$?
We will prove globality for all pointed wedges $W$ such that there exists
another wedge $W'\subseteq\n$ which is global in~$N$ and
satisfies $(W\cap{\n})\supseteq\interior_{\scriptstyle\n}(W')\cup\{0\}$.
Especially our result applies to the groups and Lorentzian wedges considered by
Levichev and Levicheva in this volume. As another application,
we solve the globality problem of the Heisenberg-algebra, i.e. we give a
complete characterization of all Lie-wedges that are global in the
Heisenberg-group.