Stabilizers of subspaces under similitudes of the Klein quadric, and automorphisms of Heisenberg algebras
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 \(L\).
scientific article; zbMATH DE number 6053093
scientific article