$k$-step nilpotent symplectic Lie algebras associated with graphs

TL;DR

This paper constructs families of $k$-step nilpotent symplectic Lie algebras linked to graphs, generalizing previous 2-step cases and demonstrating their existence under certain conditions.

Contribution

It extends the construction of nilpotent symplectic Lie algebras from 2-step to $k$-step cases associated with graphs, broadening the class of known structures.

Findings

Constructed $k$-step nilpotent symplectic Lie algebras from graphs.

Extended previous 2-step constructions to general $k$-step cases.

Proved existence of such algebras under mild conditions.

Abstract

We construct families of $k$-step nilpotent symplectic Lie algebras associated with graphs, extending the construction given in [Pouseele-Tirao, JPAA 213 (2009)] for the 2-step case. We also show that, under mild conditions on the nilpotency type, there exist symplectic Lie algebras of that type.