Rota-Baxter type $H$-operators on pseudoalgebras

TL;DR

This paper introduces Rota-Baxter type $H$-operators on $H$-pseudoalgebras, explores their properties, and demonstrates their use in constructing various algebraic structures and analyzing related algebras.

Contribution

It defines and studies Rota-Baxter type $H$-operators on $H$-pseudoalgebras, providing foundational properties, examples, and applications in algebra construction.

Findings

Construction of associative, Lie, and NS-$H$-pseudoalgebras using Rota-Baxter type operators

Analysis of Rota-Baxter type operators on rank one $H$-pseudoalgebras

Discussion of induced annihilation and $H$-conformal algebras

Abstract

Let $H$ be a Hopf algebra. In this paper, we study a class of $H$-operators on $H$-pseudoalgebras, which resemble the Rota-Baxter $H$-operator, and they are called Rota-Baxter type $H$-operators. We firstly present some basic properties and examples. Then by using Rota-Baxter type $H$-operators, we construct a number of associative (resp. Lie, NS-) $H$-pseudoalgebras. Meanwhile, Rota-Baxter type $H$-operators on $H$-pseudoalgebras of rank one are studies respectively. Finally, we consider the annihilation algebras and $H$-conformal algebras induced by $H$-pseudoalgebras and corresponding Rota-Baxter type operators are discussed.