Related papers: Logarithmic forms with twisted coefficients

Generalising a previous work of Jiang and Sheng, a cohomology theory for differential Lie algebras of arbitrary weight is introduced. The underlying $L_\infty[1]$-structure on the cochain complex is also determined via a generalised version…

Let g be a differential graded Lie algebra and suppose given a contraction of chain complexes of g onto a general chain complex M. We show that the data determine an sh-Lie algebra structure on M, that is, a coalgebra perturbation of the…

In this paper we calculate the Hochschild cohomology of gentle $A_\infty$-algebras of arc collections on marked surfaces without boundary components. When the underlying arc collection has no loops or two-cycles, we show that the dgla…

Of four types of Kaplansky algebras, type-2 and type-4 algebras have previously unobserved $\mathbb{Z}/2$-gradings: nonlinear in roots. A method assigning a simple Lie superalgebra to every $\mathbb{Z}/2$-graded simple Lie algebra in…

Let $k$ be an arbitrary field and $d$ a positive integer. For each degenerate symmetric or antisymmetric bilinear form $M$ on $k^{d}$ we determine the structure of the Lie algebra of matrices that preserve $M$, and of the Lie algebra of…

For any Lie algebroid A, its 1-jet bundle JA is a Lie algebroid naturally and there is a representation \pi: JA ->DA. Denote by dJ the corresponding coboundary operator. In this paper, we realize the deformation cohomology of a Lie…

In this review article, first we give the concrete formulas of representations and cohomologies of associative algebras, Lie algebras, pre-Lie algebras, Leibniz algebras and 3-Lie algebras and some of their strong homotopy analogues. Then…

We construct a cohomology theory controlling the deformations of a general Drinfel'd algebra. The picture presented here has two sides -- the combinatorial one related with the fact of the existence of a graded Lie algebra structure on the…

In this article, we will explore the fundamental concepts, including various basic concepts on $d$-complex manifolds, along with several differential operators and examine the relationships between them. A $d$-K\"ahler manifold is a…

In this paper, we prove a $\partial\bar{\partial}$-type lemma on compact K\"ahler manifolds for logarithmic differential forms valued in the dual of a certain pseudo-effective line bundle, thereby confirming a conjecture proposed by X. Wan.…

We prove a converse theorem for a family of L functions of degree 2 with gamma factor coming from a holomorphic cuspform. We show these L functions coincide with either those coming from a newform or a product of L functions arising from…

A quasi-isomorphism of differential graded algebras (DGA) is a multiplicative map inducing an isomorphism on cohomology. A DGA is called formal if it can be connected by a chain of quasi-isomorphisms to its cohomology algebra. We prove that…

Suppose $(X,\omega)$ is a compact K\"ahler manifold of dimension $n$, and $\theta$ is closed $(1,1)$-form representing a big cohomology class. We introduce a metric $d_1$ on the finite energy space $\mathcal{E}^1(X,\theta)$, making it a…

An associative algebra is nothing but an odd quadratic codifferential on the tensor coalgebra of a vector space, and an A-infinity algebra is simply an arbitrary odd codifferential. Hochschild cohomology classifies the deformations of an…

In this paper we investigate the class of the connected graded algebras which are finitely generated in degree 1, which are finitely presented with relations of degrees greater or equal to 2 and which are of finite global dimension D and…

We establish H\"ormander-type $L^2$-estimates for the $\overline{\partial}$-operators that hold uniformly for all nontrivial flat holomorphic line bundles on compact K\"ahler manifolds. Our result can be regarded as a…

We study Lie algebra $\kappa$-deformed Euclidean space with undeformed rotation algebra $SO_a(n)$ and commuting vectorlike derivatives. Infinitely many realizations in terms of commuting coordinates are constructed and a corresponding star…

We describe a differential graded Lie algebra controlling infinitesimal deformations of triples $(X,\mathcal{F},\sigma)$, where $\mathcal{F}$ is a coherent sheaf on a smooth variety $X$ over a field of characteristic 0 and $\sigma\in…

Andreotti-Vesentini, Ohsawa, Gromov, Koll\'ar, among others, have observed that Hodge theory could be extended to (non compact) K\"ahler complete manifolds, within the L^2 framework. Also, many vanishing theorems on projective or K\"ahler…

Any finite-dimensional commutative (associative) graded algebra with all nonzero homogeneous subspaces one-dimensional is defined by a symmetric coefficient matrix. This algebraic structure gives a basic kind of $A$-graded algebras…