Cocommutative Com-PreLie bialgebras
Rings and Algebras
2025-05-15 v2
Abstract
A Com-PreLie bialgebra is a commutative bialgebra with an extra preLie product satisfying some compatibilities with the product and coproduct. We here give a classification of connected, cocommutative Com-PreLie bialgebras over a field of characteristic zero: we obtain a main family of symmetric algebras on a space V of any dimension, and another family available only if V is one-dimensional. We also explore the case of Com-PreLie bialgebras over a group algebra and over a tensor product of a group algebra and of a symmetric algebra.
Cite
@article{arxiv.1802.08171,
title = {Cocommutative Com-PreLie bialgebras},
author = {Loïc Foissy},
journal= {arXiv preprint arXiv:1802.08171},
year = {2025}
}