19 citations · 38 across the 8 of their papers we have counts for
10 papers
Balanced infinitesimal bialgebras, double Poisson gebras and pre-Calabi-Yau algebras
Alexandre Quesney
We consider the properad that governs the balanced infinitesimal bialgebras equipped with a coproduct of degree . This properad naturally encodes a part of the structure of th…
What is the Magnus Expansion?
Kurusch Ebrahimi-Fard, Igor Mencattini, Alexandre Quesney
The Magnus expansion, introduced by Wilhelm Magnus in 1954, is an infinite Lie series employed to express solutions for first-order homogeneous linear differential equations involv…
Crossed morphisms, (integration of) post-Lie algebras and the post-Lie Magnus expansion
Igor Mencattini, Alexandre Quesney
In the first part of this letter it will be shown that the post-Lie Magnus expansion can be interpreted as a crossed morphism between two (local) Lie group. The second part will be…
Post-symmetric braces and integration of post-Lie algebras
Igor Mencattini, Alexandre Quesney, Pryscilla Silva
In this paper we identify the post-Lie analogue of the symmetric brace algebras, advocate their role in the theory of the associated D-algebras and present some relations with the…
The quantum trace as a quantum non-abelianization map
Julien Korinman, Alexandre Quesney
We prove that the balanced Chekhov-Fock algebra of a punctured triangulated surface is isomorphic to a skein algebra which is a deformation of the algebra of regular functions of s…
Classical shadows of stated skein representations at roots of unity
Julien Korinman, Alexandre Quesney
We extend some results of Bonahon, Bullock, Turaev and Wong concerning the skein algebras of closed surfaces to L^e's stated skein algebra associated to open surfaces. We prove tha…
On the deformation complex of homotopy affine actions
Eduardo Hoefel, Muriel Livernet, Alexandre Quesney
An affine action of an associative algebra on a vector space is an algebra morphism , where is a vector space and …
The relative lattice path operad
Alexandre Quesney
We construct a set-theoretic coloured operad that may be thought of as a combinatorial model for the Swiss Cheese operad. This is the relative (or Swiss Cheese) version of the latt…
On the homology of the double cobar construction of a double suspension
Alexandre Quesney
The double cobar construction of a double suspension comes with a Connes-Moscovici structure, that is a homotopy G-algebra (or Gerstenhaber-Voronov algebra) structure together with…
Homotopy BV-algebra structure on the double cobar construction
Alexandre Quesney
We show that the double cobar construction, , of a simplicial set is a homotopy BV-algebra if is a double suspension, or if is 2-reduced and the coefficient…