9 citations · 63 across the 28 of their papers we have counts for
5 papers · 1 filter
On deformation theory and graph homology
Fusun Akman, Lucian M. Ionescu, Papa A. Sissokho
Deformation theory of associative algebras and in particular of Poisson algebras is reviewed. The role of an almost contraction leading to a canonical solution of the corresponding…
A canonical semi-classical star-product
Lucian M. Ionescu, Papa A. Sissokho
We study the Maurer-Cartan equation of the pre-Lie algebra of graphs controling the deformation theory of associative algebras and prove that there is a canonical solution within t…
Cohomology of Feynman graphs and perturbative quantum field theory
Lucian M. Ionescu
An analog of Kreimer's coproduct from renormalization of Feynman integrals in quantum field theory, endows an analog of Kontsevich's graph complex with a dg-coalgebra structure. Th…
Graph complexes in deformation quantization
Domenico Fiorenza, Lucian M. Ionescu
Kontsevich's formality theorem and the consequent star-product formula rely on the construction of an -morphism between the DGLA of polyvector fields and the DGLA of poly…
Higher Derived Brackets and Deformation Theory I
Fusun Akman, Lucian M. Ionescu
The existing constructions of derived Lie and sh-Lie brackets involve multilinear maps that are used to define higher order differential operators. In this paper, we prove the equi…