论文标题
$ v $ -Universal Hopf代数（CO）作用于$ω$ -Algebras
$V$-universal Hopf algebras (co)acting on $Ω$-algebras
论文作者
论文摘要
我们开发了一种理论，该理论统一了由Sweedler，Manin和Tambara研究的通用（CO）代表代数，并与最近引入的\ cite {AGV1} BI/HOPF-Elgebras一起统一了所有支持（CO）ACTIC BI/HOPF Algebras。我们的方法使用向量空间，并在$ a $ a $ a $ a $ a $ a $ a $ a $ algebras之间具有线性图系列。这使我们能够以统一的方式对待代数，煤桥，编织矢量空间和许多其他结构。我们研究了$ v $ - 宇宙测量煤层和$ v $ - 宇宙在$ω$ -Algebras $ a $和$ b $之间的代数，相对于固定的子空间$ v $ of $ \ vect（a，b）$。通过考虑$ a = b $的情况，我们以给定代数$ a $的价格得出了$ v $ umiversal（CO）代理Bialgebra（和Hopf代数）的概念。特别是，这导致了Manin-tambara通用bi/hopf代数的存在条件的改进。我们在某些条件下，在$ \\ end_f（a）$的有限拓扑中，在某些条件下，在某些条件下，$ v $ umiversal bi/hopf代数在$ \ end_f（a）$之间建立了$ v $ - 宇宙代理BI/HOPF代数与$ v $ umiversal cocting BI/HOPF代数之间的同构。
We develop a theory which unifies the universal (co)acting bi/Hopf algebras as studied by Sweedler, Manin and Tambara with the recently introduced \cite{AGV1} bi/Hopf-algebras that are universal among all support equivalent (co)acting bi/Hopf algebras. Our approach uses vector spaces endowed with a family of linear maps between tensor powers of $A$, called $Ω$-algebras. This allows us to treat algebras, coalgebras, braided vector spaces and many other structures in a unified way. We study $V$-universal measuring coalgebras and $V$-universal comeasuring algebras between $Ω$-algebras $A$ and $B$, relative to a fixed subspace $V$ of $\Vect(A,B)$. By considering the case $A=B$, we derive the notion of a $V$-universal (co)acting bialgebra (and Hopf algebra) for a given algebra $A$. In particular, this leads to a refinement of the existence conditions for the Manin--Tambara universal coacting bi/Hopf algebras. We establish an isomorphism between the $V$-universal acting bi/Hopf algebra and the finite dual of the $V$-universal coacting bi/Hopf algebra under certain conditions on $V$ in terms of the finite topology on $\End_F(A)$.
