Related papers: Unified products for alternative and pre-alternati…
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…
The extending structures and unified products for Zinbiel algebras are developed. Some special cases of unified products such as crossed products and matched pair of Zinbiel algebras are studied. It is proved that the extending structures…
The extending structures and unified products for Malcev algebras are developed. Some special cases of unified products such as crossed products and matched pair of Malcev algebras are studied. It is proved that the extending structures can…
The extending structures problem for Zinbiel 2-algebras is studied. We introduce the concept of unified products for Zinbiel 2-algebras. Some special cases of unified products such as crossed product and matched pair of Zinbiel 2-algebras…
We introduce the concept of braided alternative bialgebra. The theory of cocycle bicrossproducts for alternative bialgebras is developed. As an application, the extending problem for alternative bialgebra is solved by using some non-abelian…
In this paper, we give a study of the $\mathbb{C}[\partial]$-split extending structures problem for associative conformal algebras. Using the unified product as a tool, which includes interesting products such as bicrossed product, cocycle…
The aim of this paper is to provide an answer to the $\mathbb{C}[\partial]$-split extending structures problem for Leibniz conformal algebras, which asks that how to describe all Leibniz conformal algebra structures on $E=R\oplus Q$ up to…
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…
Let $A$ be a left-symmetric (resp. Novikov) algebra, $E$ be a vector space containing $A$ as a subspace and $V$ be a complement of $A$ in $E$.The extending structures problem which asks for the classification of all left-symmetric (resp.…
We introduce the concept of braided noncommutative Poisson bialgebras. The theory of cocycle bicrossproducts for noncommutative Poisson bialgebras is developed. As an application, we solve the extending problem by using some non-abelian…
In this paper, we devote to extending structures for dendriform algebras. First, we define extending datums and unified products of dendriform algebras, and theoretically solve the extending structure problem. As an application, we consider…
We introduce the concept of braided anti-flexible bialgebra and construct cocycle bicrossproduct anti-flexible bialgebras. As an application, we solve the extending problem for anti-flexible bialgebras by using some non-abelian cohomology…
Different (fibrewise) amalgamated products of continuous C*-bundles have been studied over the last years, one of the main question being to know when these amalgamated products are continuous C*-bundles. In order to gather these approaches…
We introduce the concept of braided BiHom-Frobenius algebras and give the cocycle bicrossproduct construction for BiHom-Frobenius algebras. We find that the extending problem for BiHom-Frobenius algebras can be classified by non-abelian…
In this paper, we first explore the extending structures problem by the unified product for anti-dendriform algebras. In particular,the crossed product and non-abelian extension are studied. Furthermore, we explore the inducibility problem…
We introduce the concept of braided left-symmetric bialgebras and construct cocycle bicrossproduct left-symmetric bialgebras. As an application, we solve the extending problem for left-symmetric bialgebras by using some non-abelian…
We develop the deformation theory of A_\infty algebras together with \infty inner products and identify a differential graded Lie algebra that controls the theory. This generalizes the deformation theories of associative algebras, A_\infty…
The aim of this paper is to deal with BiHom-alternative algebras which are a generalization of alternative and Hom-alternative algebras, their structure is defined with two commuting multiplicative linear maps. We study cohomology and…
We introduce a notion of pre-alternative algebra which may be seen as an alternative algebra whose product can be decomposed into two pieces which are compatible in a certain way. It is also the "alternative" analogue of a dendriform…
Non-abelian tensor product of Hom-Lie algebras is constructed and studied. This tensor product is used to describe universal ($\alpha$-)central extensions of Hom-Lie algebras and to establish a relation between cyclic and Milnor cyclic…