Stabilizers of subspaces under similitudes of the Klein quadric, and automorphisms of Heisenberg algebras (Q432734)

The authors study nilpotent Lie algebras \(L\) of class 2 with the property that \(\dim (L/[L,L]) =4\). Algebras of this type were classified by the second author in [J. Lie Theory 18, No. 2, 391--411 (2008; Zbl 1179.17013)] by a geometric approach using the action of \(\mathrm{GL}(L/[L,L])\) on the Klein quadric. In the paper under review, the authors use the same setting to determine the automorphism group \(\Aut(L)\) of \(L\) and the orbits of \(\Aut(L)\) on \(L\).