A Global version of Grozman's theorem

TL;DR

This paper extends Grozman's theorem to classify all equivariant bilinear maps between tensor density modules over the circle, removing the differential operator restriction and exploring algebraic geometry contexts.

Contribution

It provides a full classification of equivariant bilinear maps on the circle without assuming they are differential operators, broadening Grozman's original results.

Findings

Classification of all equivariant bilinear maps on the circle

Extension beyond differential operator constraints

Application to algebraic geometry setting

Abstract

Let X be a manifold. The classification of all equivariant bilinear maps between tensor density modules over X has been investigated by Yu Grozman, who has provided a full classification for those which are differential operators. Here, we investigate the same question without the hypothesis that the maps are differential operators. In our paper, the geometric context is algebraic geometry and the manifold X is the circle Spec C[z,z^{-1}].