论文标题
双交叉双脱块和相关结构
Double crossed biproducts and related structures
论文作者
论文摘要
令$ h $为bialgebra。令$σ：h \ otimes h \ to $是线性地图，其中$ a $是左$ h $ compodule calgebra和一个带有左$ h $ h $ - weak action $ \ triangleright $的代数。令$τ：h \ otimes h \ to b $为线性地图，其中$ b $是正确的$ h $ compodule calgebra，还有一个具有正确的$ h $ weak-weak action $ \ triangleleft $的代数。在本文中，我们改善了双面交叉产品代数的必要条件b _ {[0]} \ triangleleft a _ { - 1} = a \ otimes b $在majid的双双核电（或双 - 验化）中是必要条件之一。另一方面，我们通过Brzezński的交叉产品提供了更通用的两侧交叉产品代数结构，并提供了一些应用。
Let $H$ be a bialgebra. Let $σ: H\otimes H\to A$ be a linear map, where $A$ is a left $H$-comodule coalgebra, and an algebra with a left $H$-weak action $\triangleright$. Let $τ: H\otimes H\to B$ be a linear map, where $B$ is a right $H$-comodule coalgebra, and an algebra with a right $H$-weak action $\triangleleft$. In this paper, we improve the necessary conditions for the two-sided crossed product algebra $A\#^σ H~{^τ\#} B$ and the two-sided smash coproduct coalgebra $A\times H\times B$ to form a bialgebra (called double crossed biproduct) such that the condition $b_{[1]}\triangleright a_0\otimes b_{[0]}\triangleleft a_{-1}=a\otimes b$ in Majid's double biproduct (or double-bosonization) is one of the necessary conditions. On the other hand, we provide a more general two-sided crossed product algebra structure via Brzezński's crossed product and give some applications.
