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The Lie theory of connected pro-Lie groups : a structure theory for pro-Lie algebras, pro-Lie groups, and connected locally compact groups by Karl H. Hofmann and Sidney A. Morris is a nonfiction available to read on EtoBox.

What is The Lie theory of connected pro-Lie groups : a structure theory for pro-Lie algebras, pro-Lie groups, and connected locally compact groups about?

Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonné quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them. If a complete topological group $G$ can be approximated by Lie groups in the sense that every identity neighborhood $U$ of $G$ contains a normal subgroup $N$ such that $G/N$ is a Lie group, then it is called a pro-Lie group. Every locally compact connected topological group and every compact group is a pro-Lie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of pro-Lie groups is. For half a century, locally compact pro-Lie groups have drifted through the literature, yet this is the first book which systematically treats the Lie and structure theory of pro-Lie groups irrespective of local compactness. This study fits very well into the current trend which addresses infinite-dimensional Lie groups. The results of this text are based on a theory of pro-Lie algebras which parallels the structure theory of finite-dimensional real Lie algebras to an astonishing degree, even though it has had to overc

Who reads The Lie theory of connected pro-Lie groups : a structure theory for pro-Lie algebras, pro-Lie groups, and connected locally compact groups?

Author

Karl H. Hofmann and Sidney A. Morris

Publisher

European Mathematical Society, Thomas Hintermann

Published

2007

Language

EN

ISBN

9783037195321

Category

nonfiction

Subjects

Mathematics, Stem