An introduction to string Lie theory
The concept of so-called ``string Lie groups'' for treating models of infinite dimensional Lie groups is introduced. A string Lie group is defined as a topological Lie group \(G\) for which there exists a ``good'' family \(\Lambda (G)\) of one-parameter subgroups. The main aim of string Lie theory is to introduce a suitable topological structure on \(\Lambda (G)\) and to find procedures enabling one to recover (locally) \(G\) from \(\Lambda (G)\). In the paper under review only the basic ideas of string Lie theory are explained providing sketches of proofs and illustrating them by examples. In particular, the following problems are considered: Groups of strings. The group of strings over a Lie algebra. String groups. Abelian string Lie groups. Linear groups of strings. It is announced that a more comprehensive presentation of string Lie theory will be presented in the two forthcoming papers of the author (``Group of strings'' and ``Banach string Lie groups'') which are submitted for publication.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00016].
scientific article; zbMATH DE number 1686807