17 citations · 77 across the 17 of their papers we have counts for
18 papers
Lie and pre-Lie theory of Novikov algebras
Ruggero Bandiera, Frédéric Patras
Novikov algebras provide a simple but powerful algebraic axiomatization of important features of classical diferential calculus. We study their structure properties, modeling their…
Kapranov algebras
Ruggero Bandiera, Seokbong Seol, Mathieu Stiénon +1
Given any Kähler manifold , Kapranov discovered an algebra structure on . Motivated by this result, we introduce, as a generalization o…
Semiregularity maps and deformations of modules over Lie algebroids
Ruggero Bandiera, Emma Lepri, Marco Manetti
We determine a DG-Lie algebra controlling deformations of a locally free module over a Lie algebroid . Moreover, for every flat inclusion of Lie algebroids $\mathcal{A…
liftings of semiregularity maps via Chern-Simons classes
Ruggero Bandiera, Emma Lepri, Marco Manetti
We introduce the notion of Chern-Simons classes for curved DG-pairs and we prove that a particular case of this general construction provides canonical liftings of Buchw…
Cumulants, Koszul brackets and homological perturbation theory for commutative and algebras
Ruggero Bandiera
We explore the relationship between the classical constructions of cumulants and Koszul brackets, showing that the former are an expontial version of the latter. Moreover, under so…
A closed-formula solution to the color-trace decomposition problem
Ruggero Bandiera, Carlos R. Mafra
In these notes we present a closed-formula solution to the problem of decomposing traces of Lie algebra generators into symmetrized traces and structure constants. The solution is…
Formality conjecture for minimal surfaces of Kodaira dimension 0
Ruggero Bandiera, Marco Manetti, Francesco Meazzini
Let F be a polystable sheaf on a smooth minimal projective surface of Kodaira dimension 0. Then the DG-Lie algebra RHom(F,F) of derived endomorphisms of F is formal. The proof is b…
Deformations of polystable sheaves on surfaces: quadraticity implies formality
Ruggero Bandiera, Marco Manetti, Francesco Meazzini
We study relations between the quadraticity of the Kuranishi family of a coherent sheaf on a complex projective scheme and the formality of the DG-Lie algebra of its derived endomo…
Polyvector fields and polydifferential operators associated with Lie pairs
Ruggero Bandiera, Mathieu Stiénon, Ping Xu
We prove that the spaces and $\operatorname{tot}\big(Γ(Λ^\bullet A^\vee)\otime…
Shifted derived Poisson manifolds associated with Lie pairs
Ruggero Bandiera, Zhuo Chen, Mathieu Stiénon +1
We study the shifted analogue of the "Lie--Poisson" construction for algebroids and we prove that any algebroid naturally gives rise to shifted derived Poisso…
Descent of Deligne-Getzler -groupoids
Ruggero Bandiera
We prove that Getzler's higher generalization of the Deligne groupoid commutes with totalization and homotopy limits.
Eulerian idempotent, pre-Lie logarithm and combinatorics of trees
Ruggero Bandiera, Florian Schaetz
The aim of this paper is to bring together the three objects in the title. Recall that, given a Lie algebra , the Eulerian idempotent is a canonical projection from t…
How to discretize the differential forms on the interval
Ruggero Bandiera, Florian Schaetz
We provide explicit quasi-isomorphisms between the following three algebraic structures associated to the unit interval: i) the commutative dg algebra of differential forms, ii) th…
A trick to compute certain Manin products of operads
Ruggero Bandiera
We describe simple tricks to compute the Manin black products with the operads , and .
Algebraic models of local period maps and Yukawa algebras
Ruggero Bandiera, Marco Manetti
We describe some L-infinity model for the local period map of a compact Kaehler manifold. Applications include the study of deformations with associated variation of Hodge structur…
Formality of Kapranov's brackets in Kähler geometry via pre-Lie deformation theory
Ruggero Bandiera
We recover some recent results by Dotsenko, Shadrin and Vallette on the Deligne groupoid of a pre-Lie algebra, showing that they follow naturally by a pre-Lie variant of the PBW Th…
Nonabelian higher derived brackets
Ruggero Bandiera
Let M be a graded Lie algebra, together with graded Lie subalgebras L and A such that as a graded space M is the direct sum of L and A, and A is abelian. Let D be a degree one deri…
On coisotropic deformations of holomorphic submanifolds
Ruggero Bandiera, Marco Manetti
We describe the differential graded Lie algebras governing Poisson deformations of a holomorphic Poisson manifold and coisotropic embedded deformations of a coisotropic holomorphic…