Universal enveloping H-pseudoalgebras of DGP pseudoalgebras

TL;DR

This paper develops the theory of differential graded Poisson H-pseudoalgebras, introduces their universal enveloping algebras, and explores their tensor product closure and homomorphisms within a pseudotensor category.

Contribution

It constructs universal enveloping H-pseudoalgebras for DGP pseudoalgebras and establishes their properties and homomorphisms, extending the framework of Poisson pseudoalgebras.

Findings

DGP pseudoalgebras are closed under tensor product with compatibility conditions.

Universal enveloping H-pseudoalgebras are constructed via a $\

A unique differential graded pseudoalgebra homomorphism is established.

Abstract

The notions of Poisson $H$-pseudoalgebras are generalizations of Poisson algebras in a pseudotensor category $\mathcal{M}^{\ast}(H)$. This paper introduces an analogue of Poisson-Ore extension in Poisson $H$-pseudoalgebras. Poisson $H$-pseudoalgebras with the differential graded setting induces the notions of differential graded Poisson $H$-pseudoalgebras (DGP pseudoalgebras, for short). The DGP pseudoalgebra with some compatibility conditions is proved to be closed under tensor product. Furthermore, the universal enveloping $H$-pseudoalgebras of DGP pseudoalgebras are constructed by a $\mathcal{P}$-triple. A unique differential graded pseudoalgebra homomorphism between a universal enveloping $H$-pseudoalgebra of a DGP pseudoalgebra and a $\mathcal{P}$-triple of a DGP pseudoalgebra is obtained.