Morphisms, direct sums and tensor products of K\"ahler-Poisson algebras

TL;DR

This paper introduces morphisms, direct sums, and tensor products for K"ahler-Poisson algebras, establishing their properties and providing examples to illustrate these new algebraic structures.

Contribution

It defines morphisms of K"ahler-Poisson algebras and explores their algebraic properties, including conditions for isomorphism, and introduces direct sums and tensor products.

Findings

Conditions for algebra isomorphism based on metrics

Definitions and properties of direct sums and tensor products

Illustrative examples of the new concepts

Abstract

In this paper we introduce the concept of morphisms of K\"ahler-Poisson algebras and study their algebraic properties. In particular, we find conditions, in terms of the metric, for two algebras to be isomorphic, and we introduce direct sums and tensor products of K\"ahler-Poisson algebras. We provide detailed examples to illustrate the novel concepts.