Nonexistence of invariant symmetric forms on generalized Jacobson-Witt algebras revisited

TL;DR

This paper proves that invariant symmetric bilinear forms on simple modular generalized Jacobson-Witt algebras are trivial, using homological and deformation-theoretic methods, and extends the analysis to contact type Lie algebras.

Contribution

It offers a new homological proof of the nonexistence of such forms and explores their structure on contact type Lie algebras.

Findings

Invariant symmetric bilinear forms vanish on generalized Jacobson-Witt algebras

Homological argument provides a concise proof

Deformation theory describes forms on contact type Lie algebras

Abstract

We provide a short alternative homological argument showing that any invariant symmetric bilinear form on simple modular generalized Jacobson-Witt algebras vanishes, and outline another, deformation-theoretic one, allowing to describe such forms on simple modular Lie algebras of contact type.