Classification of Category $\mathcal{J}$ Modules for Divergence Zero Vector Fields on a Torus

Yuly Billig, John Talboom

Published 2016-07-24Version 1

A family of modules for the Lie algebra of vector fields on a torus, called category $\mathcal{J}$, is defined in [1] where indecomposable modules in this category are classified. Modules in category $\mathcal{J}$ are required to admit an action by the algebra of Laurent polynomials that is compatible with that of the Lie algebra of vector fields. This paper presents an analogous category $\mathcal{J}$ for the subalgebra of divergence zero vector fields on a torus and classifies the indecomposable modules of this category.