On pseudo-bialgebras

TL;DR

This paper explores the structure of pseudo-bialgebras, introducing new concepts like Lie H-coalgebras and pseudo-bialgebras, and extends classical Lie theory results such as CYBE and Drinfeld's double to this setting.

Contribution

It defines Lie H-coalgebras and pseudo-bialgebras, and generalizes classical Lie algebra structures and theorems to the pseudoalgebra context.

Findings

Introduction of Lie H-coalgebras and pseudo-bialgebras

Extension of CYBE, Manin triples, and Drinfeld's double to pseudo-bialgebras

Description of the annihilation algebra as a convolution algebra

Abstract

We study pseudoalgebras from the point of view of pseudo-dual of classical Lie coalgebra structures. We define the notions of Lie H-coalgebra and Lie pseudo-bialgebra. We obtain the analog of the CYBE, the Manin triples and Drinfeld's double for Lie pseudo-bialgebras. We also get a natural description of the annihilation algebra associated to a pseudoalgebra as a convolution algebra, clarifying this constructions in the theory of pseudoalgebras.