论文标题
全态生成的Hopf代数和量子谎言组
Holomorphically finitely generated Hopf algebras and quantum Lie groups
论文作者
论文摘要
我们研究拓扑HOPF代数，这些代数是有限型（HFG）作为fréchetArens的拓扑代数 - 在Pirkovskii的意义上是ichechet Arens的代数。其中一些（但不是全部）可以通过应用分析函数从Aggine Hopf代数获得。我们表明，交换性HFG HOPF代数始终是复杂的谎言组（实际上是Stein组）的全体形态函数的代数，并且证明相应的类别是等效的。 Akbarov紧凑地生成复杂的Lie Group〜 $ G $，相关联的拓扑Hopf代数，代数$ {\ Mathscr a} _ {exp}（exp}（g）的指数分析函数。我们表明它是HFG，但并非每个共同公愿的HFG Hopf代数都是这种形式。在连接$ g $的情况下，使用作者的先前结果，我们建立了$ {\ Mathscr a} _ {exp}（g）$的分析结构定理。这取决于$ g $的大规模几何形状。我们还考虑了一些有趣的示例，包括经典$ \ hbar $ - ad量子组的复杂分析类似物。
We study topological Hopf algebras that are holomorphically finitely generated (HFG) as Fréchet Arens--Micheal algebras in the sense of Pirkovskii. Some of them, but not all, can be obtained from affine Hopf algebras by applying the analytization functor. We show that a commutative HFG Hopf algebra is always an algebra of holomorphic functions on a complex Lie group (actually a Stein group), and prove that the corresponding categories are equivalent. With a compactly generated complex Lie group~$G$, Akbarov associated a cocommutative topological Hopf algebra, the algebra ${\mathscr A}_{exp}(G)$ of exponential analytic functionals. We show that it is HFG but not every cocommutative HFG Hopf algebra is of this form. In the case when $G$ is connected, using previous results of the author we establish a theorem on the analytic structure of ${\mathscr A}_{exp}(G)$. It depends on the large-scale geometry of $G$. We also consider some interesting examples including complex-analytic analogues of classical $\hbar$-adic quantum groups.
