Continuous and Twisted L_infinity Morphisms
英文摘要：
The purpose of this paper is to develop a suitable notion of continuous L_infinity morphism between DG Lie algebras, and to study twists of such morphisms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
On L-infinity morphisms of cyclic chains
Recently the first two authors constructed an L-infinity morphism using the S^1-equivariant version of the Poisson Sigma Model (PSM). Its role in deformation quantization was not entirely clear. We give here a "good" interpretation and show that the resulting formality statement is equivalent to formality on cyclic chains as conjectured by Tsygan and proved recently by several authors.
math.QAmath.RA
The Homotopy Class of twisted $L_\infty$-morphisms
The global formality of Dolgushev depends on the choice of a torsion-free covariant derivative. We prove that the globalized formalities with respect to two different covariant derivatives are homotopic. More explicitly, we derive the statement by proving a more general homotopy equivalence between $L_\infty$-morphisms that are twisted with gauge equivalent Maurer-Cartan elements.
math-phmath.DGmath.MP
Twisted Modules of a Vertex Operator Algebra and Associators as Classifying Morphisms
The monoidal category of twisted modules of a Vertex Operator Algebra $V$ is defined and reduced to its 2-group of invertible objects $G_α$, which can be described by a 3-cocycle $α$ on its 0-truncation $G$ with values in the group of units $A$ of the field of definition of $V$ serving as its associator. This cocycle also presents the classifying morphism of an $\infty$-group extension of $G$ by the delooping $BA$. Motivated by this, it is proven that the $\infty$-group extension classified by a 3-cocycle $α$ is presented by the skeletal 2-group $G_α$ with associator $α$. The results are discu…
math.CTmath.GRmath.QA
三角双代数与扭曲态射的2-范畴中的二元积
The binary product in the 2-category of triangular bialgebras and twisted morphisms
University of Turin（都灵大学）；Université Libre de Bruxelles（布鲁塞尔自由大学）
本文在2-范畴框架下，通过引入适当的二元积概念并利用张量积双代数上的扭曲描述，将双代数张量积的二元积性质推广到三角双代数及其扭曲态射，并应用于解释三角双代数的扭曲张量积。
math.CTmath.QAmath.RA
Convolution algebras and the deformation theory of infinity-morphisms
Given a coalgebra C over a cooperad, and an algebra A over an operad, it is often possible to define a natural homotopy Lie algebra structure on hom(C,A), the space of linear maps between them, called the convolution algebra of C and A. In the present article, we use convolution algebras to define the deformation complex for infinity-morphisms of algebras over operads and coalgebras over cooperads. We also complete the study of the compatibility between convolution algebras and infinity-morphisms of algebras and coalgebras. We prove that the convolution algebra bifunctor can be extended to a b…
math.ATmath.CTmath.QA
L-infinity algebras, Cartan homotopies and period maps
We prove that, for every compact Kaehler manifold, the period map of its Kuranishi family is induced by a natural L-infinity morphism. This implies, by standard facts about L-infinity algebras, that the period map is a "morphism of deformation theories" and then commutes with all deformation theoretic constructions (e.g. obstructions).
math.AGmath.QA
更多相关论文收起更多论文
The canonical basis and the quantum Frobenius morphism
The first goal of this paper is to study the amount of compatibility between two important constructions in the theory of quantized enveloping algebras, namely the canonical basis and the quantum Frobenius morphism. The second goal is to study orders with which the Kashiwara crystal B(infinity) of a symmetrizable Kac-Moody algebra can be endowed; these orders are defined so that the transition matrices between bases naturally indexed by B(infinity) are lower triangular.
math.QAmath.RT
Homomorphisms and rigid isomorphisms of twisted group doubles
We prove several results concerning quasi-bialgebra morphisms $\mathcal{D}^ω(G)\to\mathcal{D}^η(H)$ of twisted group doubles. We take a particular focus on the isomorphisms which are simultaneously isomorphisms $\mathcal{D}(G)\to\mathcal{D}(H)$. All such isomorphisms are shown to be morphisms of quasi-Hopf algebras, and a classification of all such isomorphisms is determined. Whenever $ω\in Z^3(G/Z(G),U(1))$ this suffices to completely describe $\operatorname{Aut}(\mathcal{D}^ω(G))$, the group of quasi-Hopf algebra isomorphisms of $\mathcal{D}^ω(G)$, and so generalizes existing descriptions fo…
math.GRmath.QAmath.RA
单纯properadic同伦
Simplicial properadic homotopy
CNRS（法国国家科学研究中心）
本文解决了properad上同伦代数无穷态射的同伦性质，通过建立单纯富化构造同伦范畴实现局部化，并刻画了无穷态射类型，将operad的已知性质扩展至properad层面。
math.ATmath.CTmath.QA
Cohomology of Feynman graphs and perturbative quantum field theory
An analog of Kreimer's coproduct from renormalization of Feynman integrals in quantum field theory, endows an analog of Kontsevich's graph complex with a dg-coalgebra structure. The graph complex is generated by orientation classes of labeled directed graphs. A graded commutative product is also defined, compatible with the coproduct. Moreover, a dg-Hopf algebra is identified. Graph cohomology is defined applying the cobar construction to the dg-coalgebra structure. As an application, L-infinity morphisms represented as series over Feynman graphs correspond to graph cocycles. Notably the total…
math-phmath.MPmath.QA
Operad of formal homogeneous spaces and Bernoulli numbers
It is shown that for any morphism, i: g --> h, of Lie algebras the vector space underlying the Lie algebra h is canonically a g-homogeneous formal manifold with the action of g being highly nonlinear and twisted by Bernoulli numbers. This fact is obtained from the study of a 2-coloured operad of formal homogeneous spaces and its minimal resolution, and is used to give a new conceptual explanation of both Ziv Ran's Jacobi-Bernoulli complex and Fiorenza-Manetti's L-infinity algebra structure on the mapping cone of a morphism of two Lie algebras. All these constructions are iteratively extended t…
math.AGmath.QA
Minimal models of quantum homotopy Lie algebras via the BV-formalism
Using the BV-formalism of mathematical physics an explicit construction for the minimal model of a quantum L-infinity-algebra is given as a formal super integral. The approach taken herein to these formal integrals is axiomatic; they can be approached using perturbation theory to obtain combinatorial formulae as shown in the appendix. Additionally, there exists a canonical differential graded Lie algebra morphism mapping formal functions on homology to formal functions on the whole space. An L-infinity-algebra morphism inverse to this differential graded Lie algebra morphism on the level of ho…
hep-thmath.ATmath.QA
Hom-quasi-bialgebras
The purpose of this paper is to give a general survey of Hom-bialgebras, which are bialgebra-type structures where the identities are twisted by a morphism, and to extend the concept of quasi-bialgebra to Hom-setting. We provide some key constructions and generalize the concept of gauge transformation and Drinfeld's twists to this type of generalized quasi-bialgebras. Moreover, we provide an example of twisted quantum double.
math.QAmath.RA
L-infinity structures on mapping cones
We show that the mapping cone of a morphism of differential graded Lie algebras $χ\colon L\to M$ can be canonically endowed with an $L_\infty$-algebra structure which at the same time lifts the Lie algebra structure on $L$ and the usual differential on the mapping cone. Moreover, this structure is unique up to isomorphisms of $L_\infty$-algebras. The associated deformation functor coincides with the one introduced by the second author in arXiv:math.AG/0507287.
math.AGmath.QA
Simultaneous deformations of algebras and morphisms via derived brackets
We present a method to construct explicitly L-infinity algebras governing simultaneous deformations of various kinds of algebraic structures and of their morphisms. It is an alternative to the heavy use of the operad machinery of the existing approaches. Our method relies on Voronov's derived bracket construction.
math-phmath.MPmath.QA
An example of a braided category of C*- algebras
A braided category of C*-algebras is constructed. Its objects are C*-algebras endowed with an action of the group R, its morphisms are C*-algebras morphisms intertwining the action of R, the crossed product of its two objects essentially depends on the action of R on considered C*-algebras. Crossed products of any object with the algebra of all continuous vanishing at infinity functions on R and algebras of all continuous functions on one- and twodimensional tori are discussed.
math.QAq-alg
