In this appendix we shall record background material on abelian groups. We begin by fixing
standard notation and by listing elementary examples. Basically we stay in the domain of …

In this survey, we report on the state of the art of some of the fundamental problems in the
Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie …

Locally compact groups play an important role in many areas of mathematics as well as in
physics. The class of locally compact groups admits a strong structure theory, which allows …

Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many
different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs …

The aim of this paper is to provide a comprehensive exposition of the early contributions to
the so-called Campbell, Baker, Hausdorff, Dynkin Theorem during the years 1890–1950 …

This paper contains a survey of recent developments in the investigation of word equations
in simple matrix groups and polynomial equations in simple (associative and Lie) matrix …

Topology is an important and interesting area of mathematics, the study of which will not
only introduce you to new concepts and theorems but also put into context old ones like …

Introducing foundational concepts in infinite-dimensional differential geometry beyond
Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of …

Many infinite-dimensional Lie groups G of interest can be expressed as the union G=∪ n∈
ℕ G n of an ascending sequence G_ 1 ⊆ G_ 2 ⊆ ⋯ of (finite-or infinite-dimensional) Lie …

We show that a compact group G has finite conjugacy classes, ie, is an FC-group if and only
if its center Z (G) is open if and only if its commutator subgroup G′ is finite. Let d (G) denote …