Symplectic Structures on Free Nilpotent Lie algebras
Viviana del Barco
TL;DR
This paper investigates the conditions under which free nilpotent Lie algebras admit symplectic structures, providing criteria for even dimensions and exploring central extensions for odd dimensions.
Contribution
It offers necessary and sufficient conditions for symplectic structures on free nilpotent Lie algebras, including analysis of central extensions.
Findings
Criteria for symplectic structures in even dimensions
Conditions for central extensions in odd dimensions
Characterization of symplectic structures on free nilpotent Lie algebras
Abstract
In this work we study the problem of existence of symplectic structures on free nilpotent Lie algebras. Necessary and sufficient conditions are given for even dimensional ones. The one dimensional central extension for odd dimensional free nilpotent Lie algebras is also considered.
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