On pseudo-bialgebras

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.

arXiv admin note: substantial text overlap with arXiv:math/0007121