论文标题
关于复杂谎言组的全态反射性条件
On holomorphic reflexivity conditions for complex Lie groups
论文作者
论文摘要
我们考虑了Akbarov对复杂的谎言组的非交通性Pontryagin二重性的全体形态版本。我们证明，在假设$ g $是一个有限多个组件的Stein集团的假设，那就是（1）$ g $上的Holomorphic函数的拓扑Hopf代数在$ g $上是全晶反射，并且仅当$ g $是线性的； （2）指数分析功能上$ g $的双重共同拓扑HOPF代数是全态反射性的。我们给出一个反例，这表明第一个标准不能扩展到无限多组件的情况。尽管如此，我们猜想通常，可以根据$ g $的Banach-Elgebra线性来解决这个问题。
We consider Akbarov's holomorphic version of the non-commutative Pontryagin duality for a complex Lie group. We prove, under the assumption that $G$ is a Stein group with finitely many components, that (1) the topological Hopf algebra of holomorphic functions on $G$ is holomorphically reflexive if and only if $G$ is linear; (2) the dual cocommutative topological Hopf algebra of exponential analytic functional on $G$ is holomorphically reflexive. We give a counterexample, which shows that the first criterion cannot be extended to the case of infinitely many components. Nevertheless, we conjecture that, in general, the question can be solved in terms of the Banach-algebra linearity of $G$.
