Feynman diagrams and minimal models for operadic algebras

@article{Chuang2008FeynmanDA,
  title={Feynman diagrams and minimal models for operadic algebras},
  author={Joseph Chuang and Andrey Lazarev},
  journal={Journal of The London Mathematical Society-second Series},
  year={2008},
  volume={81},
  pages={317-337}
}
  • J. Chuang, A. Lazarev
  • Published 24 February 2008
  • Mathematics, Computer Science
  • Journal of The London Mathematical Society-second Series
We construct an explicit minimal model for an algebra over the cobar-construction of a differential graded operad. The structure maps of this minimal model are expressed in terms of sums over decorated trees. We introduce the appropriate notion of a homotopy equivalence of operadic algebras and show that our minimal model is homotopy equivalent to the original algebra. All this generalizes and gives a conceptual explanation of well-known results for A∞-algebras. Furthermore, we show that these… 
Sullivan minimal models of operad algebras
We prove the existence of Sullivan minimal models of operad algebras, for a quite wide family of operads in the category of complexes of vector spaces over a field of characteristic zero. Our
Curved infinity-algebras and their characteristic classes
In this paper, we study a natural extension of Kontsevich's characteristic class construction for A∞- and L∞-algebras to the case of curved algebras. These define homology classes on a variant of his
Koszul duality and homotopy theory of curved Lie algebras
This paper introduces the category of marked curved Lie algebras with curved morphisms, equipping it with a closed model category structure. This model structure is---when working over an
Minimal models of quantum homotopy Lie algebras via the BV-formalism
Using the BV-formalism of mathematical physics an explicit construction for the minimal model of a quantum L-infinity-algebra is given as a formal super integral. The approach taken herein to these
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 model
Maurer–Cartan moduli and models for function spaces☆
We set up a formalism of Maurer–Cartan moduli sets for L∞ algebras and associated twistings based on the closed model category structure on formal differential graded algebras (a.k.a. differential
Gauge equivalence for complete $L_\infty$-algebras
We introduce a notion of left homotopy for Maurer--Cartan elements in $L_{\infty}$-algebras and $A_{\infty}$-algebras, and show that it corresponds to gauge equivalence in the differential graded
Unbased rational homotopy theory:a Lie algebra approach
In this paper an algebraic model for unbased rational homotopy theory from the perspective of curved Lie algebras is constructed. As part of this construction a model structure for the category of
Formality Theorem for Hochschild Cochains via Transfer Belatedly to Simon Lyakhovich on the occasion of his 50th birthday
We construct a 2-colored operad Ger + which, on the one hand, extends the operad Ger∞ governing homotopy Gerstenhaber algebras and, on the other hand, extends the 2-colored operad governing
Unimodular homotopy algebras and Chern–Simons theory
Quantum Chern–Simons invariants of differentiable manifolds are analyzed from the point of view of homological algebra. Given a manifold M and a Lie (or, more generally, an L∞) algebra g, the vector
...
1
2
3
4
...

References

SHOWING 1-10 OF 44 REFERENCES
Dual Feynman transform for modular operads
We introduce and study the notion of a dual Feynman transform of a modular operad. This generalizes and gives a conceptual explanation of Kontsevich's dual construction producing graph cohomology
Modular Operads
We develop a \higher genus" analogue of operads, which we call modular operads, in which graphs replace trees in the deenition. We study a functor F on the category of modular operads, the Feynman
Cohomology theories for homotopy algebras and noncommutative geometry
This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely A∞–, C∞– and L∞–algebras. This framework is based on noncommutative geometry as
ASSOCIAHEDRA, CELLULAR W -CONSTRUCTION AND PRODUCTS OF A∞-ALGEBRAS
The aim of this paper is to construct a functorial tensor product of A∞-algebras or, equivalently, an explicit diagonal for the operad of cellular chains, over the integers, of the Stasheff
Strongly homotopy algebras of a K\"ahler manifold
It is shown that any compact K\"ahler manifold $M$ gives canonically rise to two strongly homotopy algebras, the first one being associated with the Hodge theory of the de Rham complex and the second
Symplectic C∞-algebras
In this paper we show that a strongly homotopy commutative (or C∞-) algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic C∞-algebra (an ∞-generalisation
Associahedra, cellular W-construction and products of $A_\infty$-algebras
The aim of this paper is to construct a functorial tensor product of A ∞ -algebras or, equivalently, an explicit diagonal for the operad of cellular chains, over the integers, of the Stasheff
Loop Homotopy Algebras in Closed String Field Theory
Abstract: Barton Zwiebach constructed [20] “string products” on the Hilbert space of a combined conformal field theory of matter and ghosts, satisfying the “main identity”. It has been well known
Koszul duality for Operads
(0.1) The purpose of this paper is to relate two seemingly disparate developments. One is the theory of graph cohomology of Kontsevich [Kon 2 3] which arose out of earlier works of Penner [Pe] and
...
1
2
3
4
5
...