论文标题
分析功能的代数分解在连接的复杂谎言组上及其完成为迭代分析粉碎产品
Decomposition of the algebra of analytic functionals on a connected complex Lie group and its completions into iterated analytic smash products
论文作者
论文摘要
我们表明，将复杂的谎言组$ g $分解为半领产品，从Pirkovskii的意义上将分析功能的代数，$ {\ Mathscr a}（g）$生成分析粉碎产品的代数。另外，我们发现半领产品的足够条件可以生成$ {\ mathscr a}（g）$的某些Arens-Michael完成的类似分解。主要结果是：如果连接$ g $，则其线性化将分解为迭代的半领产品（由构图系列组成，由阿贝尔因素和半神经因子组成），该产品将代数的分解诱导在$ {\ Mathscr a} $ a} $ a}（g）$中的$ {\ Mathscr a}（g）$中的分解中。考虑到极端情况，在所有Banach代数（又称Arens-Michael Envelope）的类别中的$ {\ Mathscr a}（g）$的信封和班级Pi-Algebras（本文中介绍的新概念）中的信封和信封中，我们将这些概念介绍给了这些构造，这些概念是将这些构成的产品分析，这些概念是涉及的产品。
We show that a decomposition of a complex Lie group $G$ into a semidirect product generates that of the algebra of analytic functional, ${\mathscr A}(G)$, into an analytic smash product in the sense of Pirkovskii. Also we find sufficient conditions for a semidirect product to generate similar decompositions of certain Arens-Michael completions of ${\mathscr A}(G)$. The main result: if $G$ is connected, then its linearization admits a decomposition into an iterated semidirect product (with the composition series consisting of abelian factors and a semisimple factor) that induces a decomposition of algebras in a class of completions of ${\mathscr A}(G)$ into iterated analytic smash products. Considering the extreme cases, the envelope of ${\mathscr A}(G)$ in the class of all Banach algebras (aka the Arens-Michael envelope) and the envelope in the class Banach PI-algebras (a new concept that is introduced in this article), we decompose, in particular, these envelopes into iterated analytic smash products.
