The Structure of Compact Groups
By K. Hofmann, Sidney A. Morris. 2020
547 citations recorded by the source corpus.
The theme of this book is the Structure Theory of compact groups. It contains a completely selfcontained introduction to linear Lie groups and a substantial body of material on compact Lie groups. The authors’ approach is distinctive in so far as they define a linear Lie group as a particular subgroup of the multiplicative group of a Banach algebra. Compact Lie groups are recognized at an early stage as being linear Lie groups. This approach avoids the use of machinery on manifolds. The text is written in a style to make it accessible to the beginning graduate student with a basic knowledge in analysis, algebra, and topology. At the same time the expert will find it an excellent and rich source of information on the general structure theory of compact groups.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/f426d87947ba78a36b28d623aeefa65131593976
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
- Alexander Grigorʼyan
- Nikolay Nikolov
- C. Pittet
- D. Segal
- Wolfgang Woess
- Martin T. Barlow
- Takashi Kumagai
- Andreas Thom
Citations in the corpus
- Final group topologies, Kac-Moody groups and Pontryagin duality (2006, unknown): “[ 47, Theorem 6.25 ]), and, if α, β ∈ � and α1, β1 ∈ � have the same lengths and the same angle, there exists an element w of the Weyl group with w(α1) = α and w(β1) = β (cf.”
- Isotropic Markov semigroups on ultra-metric spaces (2013, background): “According to the Levy-Malčev theorem any Abelian profinite group A appears as the intersection of the center Z(G) and the commutant [G,G] of some compact group G, and the mapping G → A is onto; see Hofmann and Morris [30].”
- Generators and commutators in finite groups; abstract quotients of compact groups (2011, background): “This is also true if G is a connected compact group instead of profinite: indeed, such a group is divisible, hence has no nontrivial finite quotients at all ([HM], Theorem 9.”