论文标题
标量扩展Hopf代数
Scalar extension Hopf algebroids
论文作者
论文摘要
鉴于Hopf代数$ H $，Brzeziński和Militaru表明，每个编织性的YETTER-DRINFELD $ H $ H $ -MODULE代数$ A $ a $ a $ a $ a $ a $ a $ a $ a $ bialgebroid结构在Smash产品smash products algebra $ Algebra $ a \ sharp h $上产生。他们还展示了一张反码地图，使$ a \ sharp h $是Lu's Hopf代数的总代数，超过$ a $。但是，已发表的证据表明，抗模态是一种特殊情况。在本文中，展示了抗原构性特性的完整证明。此外，还提供了新的通用版本。它的输入是兼容的一对$ a $和$ a^{\ MATHRM {op}} $的编织性近雪剂 - drinfeld $ h $ h $ -odule代数，输出是一种对称的hopf elgebroid $ a \ a \ shrow h \ sharp h \ cong h \ cong h \ cong h \ sharp a^{\ mathrm} $这种构造不需要$ h $的反模型可逆。
Given a Hopf algebra $H$, Brzeziński and Militaru have shown that each braided commutative Yetter-Drinfeld $H$-module algebra $A$ gives rise to an associative $A$-bialgebroid structure on the smash product algebra $A \sharp H$. They also exhibited an antipode map making $A\sharp H$ the total algebra of a Lu's Hopf algebroid over $A$. However, the published proof that the antipode is an antihomomorphism covers only a special case. In this paper, a complete proof of the antihomomorphism property is exhibited. Moreover, a new generalized version of the construction is provided. Its input is a compatible pair $A$ and $A^{\mathrm{op}}$ of braided commutative Yetter-Drinfeld $H$-module algebras, and output is a symmetric Hopf algebroid $A\sharp H \cong H\sharp A^{\mathrm{op}}$ over $A$. This construction does not require that the antipode of $H$ is invertible.
