Representations and formal deformations of Leibniz H-pseudoalgebras

Abstract

In this paper, we first give some constructions of right (resp. left) Leibniz H-pseudoalgebras and explore the characterization of symmetric Leibniz H-pseudoalgebras. Furthermore, we introduce the notion of relative Rota-Baxter H-operator and show that a right (resp. left) Leibniz H-pseudoalgebra together with a relative Rota-Baxter H-operator gives rise to a representation of related right (resp. left) Leibniz H-pseudoalgebra. Finally, we describe the central extension and the formal deformation in terms of the corresponding second cohomology group.

Keywords:

• Cohomology
• formal deformation
• Leibniz H-pseudoalgebra
• relative Rota-Baxter H-operator

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17A32
• 17B38
• 17B56

Disclosure statement

The authors declare that they have no competing interests.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 12301023).