# Pre-Lie deformation theory

@article{Dotsenko2015PreLieDT, title={Pre-Lie deformation theory}, author={Vladimir Dotsenko and Sergey Viktorovich Shadrin and Bruno Vallette}, journal={arXiv: Quantum Algebra}, year={2015} }

In this paper, we develop the deformation theory controlled by pre-Lie algebras; the main tool is a new integration theory for pre-Lie algebras. The main field of application lies in homotopy algebra structures over a Koszul operad; in this case, we provide a homotopical description of the associated Deligne groupoid. This permits us to give a conceptual proof, with complete formulae, of the Homotopy Transfer Theorem by means of gauge action. We provide a clear explanation of this latter… Expand

#### 27 Citations

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