• Title: Metric Lie Groups: Carnot-Carathéodory Spaces from the Homogeneous Viewpoin
• Author(s) Enrico Le Donne
• Publisher: Springer (2025); eBook (Creative Commons Licensed)
• License(s): Creative Commons License (CC)
• Paperback: 496 pages
• eBook: PDF and ePub
• Language: English
• ISBN-10/ASIN: 3031988310
• ISBN-13: 978-3031988318
• Share This:  

Book Description

This Open Access textbook presents Carnot-Carathéodory spaces from the perspective of Lie Groups. Its main objective is to illustrate how these non-smooth geometries manifest in various mathematical domains, including metric geometry and geometric group theory.

• Enrico Le Donne is a mathematician and researcher who has made significant contributions to the study of Carnot groups, sub-Riemannian geometry, and other non-smooth geometries.

• Amazon

• Geometry and Topology
• Algebra, Abstract Algebra, and Linear Algebra

• Metric Lie Groups (Enrico Le Donne)
• The Mirror Site (1) - PDF

• Lie Groups and Lie Algebras (Pavel Etingof)

  This book covers from basic definitions of Lie Groups to the classification of finite-dimensional representations of semisimple Lie Algebras. Lie theory, in its own right, has become regarded as a classical branch of mathematics.

• Orbital Integrals on Reductive Lie Groups and Their Algebras

  This book is to present a complete course on global analysis topics and establish some orbital applications of the integration on topological groups and their algebras to harmonic analysis and induced representations in representation theory.

• Lie Groups (Daniel Bump)

  This book proceeds beyond the representation theory of compact Lie Groups and offers a carefully chosen range of material designed to give readers the bigger picture. It explores compact Lie groups through a number of proofs.

• Topological Groups: Yesterday, Today, Tomorrow (Sidney A. Morris)

  In 1900, David Hilbert asked whether each locally euclidean topological group admits a Lie group structure. This was the fifth of his famous 23 questions which foreshadowed much of the mathematical creativity of the twentieth century.