Stabilizers of Subspaces under Similitudes of the Klein Quadric, and Automorphisms of Heisenberg Algebras

TL;DR

This paper investigates the automorphism groups and orbit structures of certain nilpotent Lie algebras of class 2 across various fields, including challenging cases like characteristic 2, advancing understanding of their symmetries.

Contribution

It characterizes automorphism groups and orbit structures for nilpotent Lie algebras of class 2 over arbitrary fields, including characteristic 2.

Findings

Automorphism groups explicitly determined for specific Lie algebras.

Orbit classifications under automorphism group actions.

Extension of results to fields with characteristic 2.

Abstract

We determine the groups of automorphisms and their orbits for nilpotent Lie algebras of class 2 and small dimension, over arbitrary fields (including the characteristic 2 case).