Related papers: Massey products and deformations
Let $f\colon X\to Y$ be a semistable fibration between smooth complex varieties of dimension $n$ and $m$. This paper contains an analysis of the local systems of de Rham closed relative one forms and top forms on the fibers. In particular…
We establish the deformation theory of Lie groupoid morphisms, describe the corresponding deformation cohomology of morphisms, and show the properties of the cohomology. We prove its invariance under isomorphisms of morphisms. Additionally,…
The study of global deformations of Lie algebras is related to the problem of classification of simple Lie algebras over fields of small characteristic. The classification of finite-dimensional simple Lie algebras is complete over…
We relate polyhedral products of topological spaces to graph products of groups. The loop homology algebras of polyhedral products are identified with the universal enveloping algebras of the Lie algebras associated with central series of…
A cohomology theory of weighted Rota-Baxter $3$-Lie algebras is introduced. Formal deformations, abelian extensions, skeletal weighted Rota-Baxter $3$-Lie 2-algebras and crossed modules of weighted Rota-Baxter 3-Lie algebras are interpreted…
Let $A$ be a unital associative algebra over a field $k$. All unital associative algebras containing $A$ as a subalgebra of a given codimension $\mathfrak{c}$ are described and classified. For a fixed vector space $V$ of dimension…
For an untwisted affine Lie algebra we prove an embedding of any higher level Demazure module into a tensor product of lower level Demazure modules (e.g. level one in type A) which becomes in the limit (for anti-dominant weights) the…
I have chosen, in this presentation of Deformation Quantization, to focus on 3 points: the uniqueness --up to equivalence-- of a universal star product (universal in the sense of Kontsevich) on the dual of a Lie algebra, the cohomology…
Deformation quantization of Poisson manifolds is studied within the framework of an expansion in powers of derivatives of Poisson structures. We construct the Lie group associated with a Poisson bracket algebra which defines a second order…
Gauge theories are studied on a space of functions with the Moyal-Weyl product. The development of these ideas follows the differential geometry of the usual gauge theories, but several changes are forced upon us. The Leibniz rule has to be…
A family of deformed Hopf algebras corresponding to the classical maximal isometry algebras of zero-curvature N-dimensional spaces (the inhomogeneous algebras iso(p,q), p+q=N, as well as some of their contractions) are shown to have a…
In this paper, we introduce the notion of crossed homomorphisms between Lie-Yamaguti algebras and establish the cohomology theory of crossed homomorphisms via the Yamaguti cohomology. Consequently, we use this cohomology to characterize…
Deformation theory refers to an apparatus in many parts of math and physics for going from an infinitesimal (= first order) deformation to a full deformation, either formal or convergent appropriately. If the algebra being deformed is that…
We show that, in general, there exist non-vanishing triple Massey products in the cohomology with finite field coefficients of a complex hypersurface complement. In contrast, the Massey products, triple and higher, in the rational…
Modified $r$-matrices are solutions of the modified classical Yang-Baxter equation, introduced by Semenov-Tian-Shansky, and play important roles in mathematical physics. In this paper, first we introduce a cohomology theory for modified…
By means of contractions of Lie algebras, we obtain new classes of indecomposable quasi-classical Lie algebras that satisfy the Yang-Baxter equations in its reformulation in terms of triple products. These algebras are shown to arise…
For $x$ an element of a field other than $0$ or $1$, we compute the order $n$ Massey products $$\langle (1-x)^{-1}, x^{-1}, \ldots, x^{-1}, (1-x)^{-1} \rangle$$ of $n-2$ factors of $x^{-1}$ and two factors of $(1-x)^{-1}$ by embedding…
We generalize basic results relating the associated graded Lie algebra and the holonomy Lie algebra from finitely presented, commutator-relators groups to arbitrary finitely presented groups. In the process, we give an explicit formula for…
In this paper, first using the higher derived brackets, we give the controlling algebra of relative difference Lie algebras, which are also called crossed homomorphisms or differential Lie algebras of weight 1 when the action is the adjoint…
We study the relationship between the higher Massey products on the cohomology $H$ of a differential graded algebra, and the $A_\infty$ structures induced on $H$ via homotopy transfer techniques.