相关论文: Deformations of coalgebra morphisms
We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algebroid. We also have a closer look at various special cases…
The cohomology and deformation theory of 3-Lie algebras are revisited. The theory of extending structures and unified product for 3-Lie algebras are developed.It is proved that the extending structures of 3-Lie algebras can be classified by…
Theory of representations of universal algebra is a natural development of the theory of universal algebra. Morphism of the representation is the map that conserve the structure of the representation. Exploring of morphisms of the…
We study deformation of algebras with coaction symmetry of reduced algebra of discrete groups, where the deformation parameter is given continuous family of group $2$-cocycles. When the group satisfies the Baum-Connes conjecture with…
We develop here a concept of deformed algebras through three examples and an application. Deformed algebras are obtained from a fixed algebra by deformation along a family of indexes, through formal series. We show how the example of…
In order to solve two problems in deformation theory, we establish natural structures of homotopy Lie algebras and of homotopy associative algebras on tensor products of algebras of different types and on mapping spaces between coalgebras…
Hom-dendriform algebras are twisted analog of dendriform algebras and are splitting of hom-associative algebras. In this paper, we define a cohomology and deformation for hom-dendriform algebras. We relate this cohomology with the…
We define the cohomology and formal deformation theories for algebra and bialgebra categories. We suggest some approaches to finding nontrivial deformations of the categories associated to the quantum groups by the work of Lusztig.
A unified description of the relationship between the Hamiltonian structure of a large class of integrable hierarchies of equations and W-algebras is discussed. The main result is an explicit formula showing that the former can be…
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…
We consider a problem which may be viewed as an inverse one to the Schwinger realization of Lie algebra, and suggest a procedure of deforming the so-obtained algebra. We illustrate the method through a few simple examples extending…
The deformation complex of an algebra over a colored PROP P is defined in terms of a minimal (or, more generally, cofibrant) model of P. It is shown that it carries the structure of an L_\infty-algebra which induces a graded Lie bracket on…
This is a list of some problems and conjectures related to various types of algebras, that is to algebraic operads. Some comments and hints are included.
We obtain several structure results for a class of spherical subgroups of connected reductive complex algebraic groups that extends the class of strongly solvable spherical subgroups. Based on these results, we construct certain…
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
Quantum multiparameter deformation of real Clifford algebras is proposed. The corresponding irreducible representations are found.
We investigate a method of construction of central deformations of associative algebras, which we call centrification. We prove some general results in the case of Hopf algebras and provide several examples.
We study new coalgebra structures on the tensor product of two coalgebras $C$ and $D$ by twisting the tensor product coalgebra via a twist map $\Psi: C \otimes D \rightarrow D \otimes C$. We deal with the general case in which the counit of…
This paper presents a cohomological study of modified Rota-Baxter associative algebras in the presence of derivations. The Modified Rota-Baxter operator, which is a modified version and closely related to the classical Rota-Baxter operator,…
We show that three deformation functors (deformations of the product, flat deformations and deformations of the relations) assigned to an associative algebra are naturally isomorphic.