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arXiv · 2510.06934

Integration theory of Lie-graph algebras

Ricardo Campos·Bruno Vallette
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Abstract

We develop the Lie theory of Lie-admissible algebras whose product is enriched with higher operations modeled on directed graphs with a view to apply it to the deformation theories controlled by this kind of Lie algebras. We produce effective formulas for their exponential map, their gauge group structure and the action on Maurer--Cartan elements. The main motivation and range of applications lies in the deformation theory of types of bialgebras which is done in a sequel article. This work extends the case of pre-Lie algebra structures which appear in the deformation theory of operadic algebras.

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Ricardo Campos, Bruno Vallette. 2025-10-08. Integration theory of Lie-graph algebras. https://arxiv.org/abs/2510.06934

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