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
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References

SHOWING 1-10 OF 19 REFERENCES
Givental Action and Trivialisation of Circle Action
In this paper, we show that the Givental group action on genus zero cohomological field theories, also known as formal Frobenius manifolds or hypercommutative algebras, naturally arises in theExpand
Props in model categories and homotopy invariance of structures
Abstract We prove that any category of props in a symmetric monoidal model category inherits a model structure. We devote an appendix, about half the size of the paper, to the proof of the modelExpand
Spaces of algebra structures and cohomology of operads
The aim of this paper is two-fold. First, we compare two notions of a "space" of algebra structures over an operad A: 1. the classification space, which is the nerve of the category of weakExpand
Homological algebra of homotopy algebras
We define closed model category structures on different categories connected to the world of operad algebras over the category C(k) of (unbounded) complexes of k-modules: on the category of operads,Expand
On the Lie envelopping algebra of a pre-Lie algebra
We construct an associative product on the symmetric module S(L) of any pre-Lie algebra L. Then we proove that in the case of rooted trees our construction is dual to that of Connes and Kreimer. WeExpand
Homological perturbation theory for algebras over operads
We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. The main difficulty is to find a suitable notion of algebra homotopy that generalizes toExpand
Symmetric Brace Algebras
  • T. Lada, M. Markl
  • Mathematics, Computer Science
  • Appl. Categorical Struct.
  • 2005
TLDR
It is explained how symmetric braces used to describe transfers of strongly homotopy structures may be used to examine the L∞-algebras that result from a particular gauge theory for massless particles of high spin. Expand
Pre-Lie algebras and the rooted trees operad
A Pre-Lie algebra is a vector space L endowed with a bilinear product * : L \times L to L satisfying the relation (x*y)*z-x*(y*z)= (x*z)*y-x*(z*y), for all x,y,z in L. We give an explicitExpand
The deformation theory of representations of fundamental groups of compact Kähler manifolds
AbstractLet Γ be the fundamental group of a compact Kähler manifold M and let G be a real algebraic Lie group. Let ℜ(Γ, G) denote the variety of representations Γ → G. Under various conditions on ρ ∈Expand
TRANSFERRING A^ (STRONGLY HOMOTOPY ASSOCIATIVE) STRUCTURES
The aim of this simple-minded "applied" note is to give explicit formulas for transfers of Aoo-structures and related maps and homotopies in the most easy situation in which these transfers exist.Expand
...
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