On moduli spaces of K\"ahler-Poisson algebras over rational functions in two variables

Document Type : Research Paper

Author

Department of Mathematics, Link"oping University, Link"oping, Sweden.

Abstract

K\"ahler-Poisson algebras were introduced as algebraic analogues of
function algebras on K\"ahler manifolds, and it turns out that one
can develop geometry for these algebras in a purely algebraic way. A
K\"ahler-Poisson algebra consists of a Poisson algebra together with
the choice of a metric structure, and a natural question arises: For
a given Poisson algebra, how many different metric structures are
there, such that the resulting K\"ahler-Poisson algebras are
non-isomorphic? In this paper we initiate a study of such moduli
spaces of K\"ahler-Poisson algebras defined over rational functions
in two variables.

Keywords