Rota-Baxter type H-operators on pseudoalgebras

2025/10/20 by Botong Gai, Gai, Botong, Shuanhong Wang +1
Computer Science · Decision Sciences · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Fuzzy and Soft Set Theory #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2510.17222

openalex publication_date 2025/10/20 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/28

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.

Citations

• Irreducible modules over finite simple Lie pseudoalgebras IV.\n Non-primitive pseudoalgebras
• Averaging algebras, Schröder numbers, rooted trees and operads
• An Algebraic Study of Averaging Operators
• On pseudo-bialgebras

Related

• Algebra, group, and Hopf Rota-Baxter operators
• Associative H-pseudoalgebras with a semigroup
• Relative Rota--Baxter operators on groups and Hopf algebras
• Related Hom-rhizaform algebras and Rota-Baxter Operators, Hom-Rhizaform Family Algebras
• sigma, tau-Rota-Baxter operators, infinitesimal Hom-bialgebras and the associative (Bi)Hom-Yang-Baxter equation