Related papers: Log Smooth Deformation Theory via Gerstenhaber Alg…
We use homotopy operators for the $L_\infty$-algebra associated with an equivariant deformation problem in order to describe a smooth parametrization of the space of structures around a given one. Along the way we give new algebraic and…
Smooth K-functors are introduced and the smooth K-theory of locally convex algebras is developed. It is proved that the algebraic and smooth K-functors are isomorphic on the category of quasi stable real (or complex) Frechet algebras.
We consider Picard surfaces, locally symmetric varieties $S_{\Gamma}$ attached to the Lie group SU(2,1), and we construct explicit differential forms on $S_{\Gamma}$ representing Eisenstein classes, i.e. cohomology classes restricting…
We introduce the notion of (homological) G-smoothness for a complex G-variety X, where G is a connected affine algebraic group. This is based on the notion of smoothness for dg algebras and uses a suitable enhancement of the G-equivariant…
For a smooth manifold X of dimension <d we construct a homomorphism from the algebraic K-theory group in degree d of the algebra of smooth functions on X to the degree -d-1 topological K-theory of X with coefficients in C/Z. This map…
We generalise Hinich's Theorem of descent of Deligne groupoids to the case where the dgLas involved have no negative cohomology. We apply this result to study the infinitesimal deformations of a morphism $\alpha: {\mathcal F} \to {\mathcal…
We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra,…
In this paper, we review deformation, cohomology and homotopy theories of relative Rota-Baxter Lie algebras, which have attracted quite much interest recently. Using Voronov's higher derived brackets, one can obtain an $L_\infty$-algebra…
The solution of Deligne's conjecture on Hochschild cochains and the formality of the operad of little disks provide us with a natural homotopy Gerstenhaber algebra structure on the Hochschild cochains of an associative algebra. In this…
In this paper we mainly describe $\mathbb{Q}$-Gorenstein smoothings of projective surfaces with only Wahl singularities which have birational fibers. For instance, these degenerations appear in normal degenerations of the projective plane,…
In this paper, we introduce the concept of L-dendriform conformal algebras, which arise naturally from the study of $\mathcal{O}$-operators on left-symmetric conformal algebras and solutions to the conformal $S$-equation. These algebras…
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e. filiform Lie (super)algebras, into the theory of Lie algebras of order F$. Thus, the concept of filiform Lie algebras of order F is…
Based on the differential graded Lie algebra controlling deformations of an $n$-Lie algebra with a representation (called an n-LieRep pair), we construct a Lie n-algebra, whose Maurer-Cartan elements characterize relative Rota-Baxter…
Recent work ([18], [1]) has produced a complete list of weighted homogeneous surface singularities admitting smoothings whose Milnor fibre has only trivial rational homology (a "rational homology disk"). Though these special singularities…
We introduce a family of metric-deformed Heisenberg algebras $M_1$ and $M_2$, where the commutation relations are expressed directly in terms of the components of a diagonal Lorentzian metric. We show that these algebras unify several known…
We study the deformation complex of a canonical morphism $i$ from the properad of (degree shifted) Lie bialgebras $\mathbf{Lieb}_{c,d}$ to its polydifferential version $\mathcal{D}(\mathbf{Lieb}_{c,d})$ and show that it is quasi-isomorphic…
We introduce the notion of a logarithmic Landau-Ginzburg (log LG) model, which is essentially given by equipping the central degenerate fiber of the family of Landau-Ginzburg (LG) models mirror to a projective toric manifold with a natural…
This paper studies formal deformations and homotopy theory of Rota-Baxter algebras of any weight. We define an $L_\infty$-algebra, which controls simultaneous deformations of associative products and Rota-Baxter operators. As a consequence,…
In this paper, we first construct a differential graded Lie algebra that controls deformations of a Lie-Yamaguti algebra. Furthermore, a relative Rota-Baxter operator on a Lie-Yamaguti algebra is characterized as a Maurer-Cartan element in…
In this note, we use give some algebraic applications of a previous result by the author which compares the deformations parameterized by the Maurer-Cartan elements of a differential graded Lie algebra, and a differential graded Lie…