相关论文: Deformations of coalgebra morphisms
We investigate deformations of lagrangian manifolds with singularities. We introduce a complex similar to the de Rham-complex whose cohomology calculates deformation spaces. Examples of singular lagrangian varieties are presented and…
We consider deformations of finite or infinite dimensional Lie algebras over a field of characteristic 0. There is substantial confusion in the literature if one tries to describe all the non-equivalent deformations of a given Lie algebra.…
We review the open problems in the theory of deformations of zero-dimensional objects, such as algebras, modules or tensors. We list both the well-known ones and some new ones that emerge from applications. In view of many advances in…
All complex $3$-dimensional nilalgebras were described. As a corollary, all degenerations in the variety of complex $3$-dimensional nilalgebras were obtained.
A construction of the tangent dg Lie algebra of a sheaf of operad algebras on a site is presented. The requirements on the site are very mild; the requirements on the algebra are more substantial. A few applications including the…
A priori, the set of birational transformations of an algebraic variety is just a group. We survey the possible algebraic structures that we may add to it, using in particular parametrised family of birational transformations.
In this paper, we study deformations of complex structures on Lie algebras and its associated deformations of Dolbeault cohomology classes. A complete deformation of complex structures is constructed in a way similar to the Kuranishi…
A morphism Lie algebra is a triple $(\mathfrak{g}, \mathfrak{h}, \phi)$ consisting of two Lie algebras $\mathfrak{g}, \mathfrak{h}$ and a Lie algebra homomorphism $\phi : \mathfrak{g} \rightarrow \mathfrak{h}$. We define representations and…
We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra.
We extend the formality theorem of M. Kontsevich from deformations of the structure sheaf on a manifold to deformations of gerbes.
A unified method of calculating structure functions from commutation relations of deformed single-mode oscillator algebras is presented. A natural approach to building coherent states associated to deformed algebras is then deduced.
An informal discussion of how the construction problem in algebraic geometry motivates the search for formal proof methods. Also includes a brief discussion of my own progress up to now, which concerns the formalization of category theory…
We construct explicitly the symmetries of the isospectral deformations as twists of Lie algebras and demonstrate that they are isometries of the deformed spectral triples.
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 algebraically closed field of characteristic…
A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.
There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…
In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative) Poisson algebras and coefficient (noncommutative)…
In this paper we set-up a general framework for a formal deformation theory of Dirac structures. We give a parameterization of formal deformations in terms of two-forms obeying a cubic equation. The notion of equivalence is discussed in…
We construct a braided structure on the algebra of K\"ahler differential forms of a commutative algebra twisted by an endomorphism. This generalises the construction done in M. Karoubi, Quantum Methods in Algebraic Topology, see…
This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.