Automorphisms of the Weyl manifold

TL;DR

This paper studies the automorphisms of Weyl manifolds associated with symplectic manifolds, focusing on their geometric and algebraic structures, and introduces modified contact Weyl diffeomorphisms.

Contribution

It characterizes automorphisms of Weyl manifolds linked to Poincaré-Cartan classes and constructs modified contact Weyl diffeomorphisms, advancing the understanding of their geometric properties.

Findings

Automorphisms correspond to certain cohomology classes.

Construction of modified contact Weyl diffeomorphisms.

Connection between Weyl manifolds and star products.

Abstract

Assume that $M$ is a smooth manifold with a symplectic structure $\omega$. Then Weyl manifolds on the symplectic manifold $M$ are Weyl algebra bundles endowed with suitable transition functions. From the geometrical point of view, Weyl manifolds can be regarded as geometrizations of star products attached to $(M,\omega)$. In the present paper, we are concerned with the automorphisms of the Weyl manifold corresponding to Poincar\'e-Cartan class ($c_0$ is a $\check{\rm C}$ech cocycle corresponding to the symplectic structure $\omega$.) $[c_0+\sum_{\ell=1}^\infty c_{\ell} \nu^{2\ell}]\in \check{H}^2 (M)[[\nu^2]]$. We also construct modified contact Weyl diffeomorphisms.