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arXiv · 1802.08171

Cocommutative Com-PreLie bialgebras

Loïc Foissy
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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.

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Loïc Foissy. 2018-02-21. Cocommutative Com-PreLie bialgebras. https://arxiv.org/abs/1802.08171

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