局部指数李代数的非标准壳
Nonstandard Hulls of Locally Exponential Lie Algebras
摘要：
给出了如何构造一类无限维李代数的非标准壳，推广了Pestov关于Banach-李代数可扩性的一个定理.在这个过程中，我们考虑了局部凸空间之间的函数的非标准光滑性条件，以保证非标准壳之间的诱导函数是光滑的。本文还讨论了局部凸空间之间的函数的非标准扩张映射为有限点到有限点的条件。
英文摘要：
We show how to construct the nonstandard hull of certain infinite-dimensional Lie algebras in order to generalize a theorem of Pestov on the enlargeability of Banach-Lie algebras. In the process, we consider a nonstandard smoothness condition on functions between locally convex spaces to ensure that the induced function between the nonstandard hulls is smooth. We also discuss some conditions on a function between locally convex spaces which guarantee that its nonstandard extension maps finite points to finite points.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
