Theory of Lie GroupsCourier Dover Publications, 30 mars 2018 - 224 pages "Chevalley's most important contribution to mathematics is certainly his work on group theory. . . . [Theory of Lie Groups] was the first systematic exposition of the foundations of Lie group theory consistently adopting the global viewpoint, based on the notion of analytic manifold. This book remained the basic reference on Lie groups for at least two decades." — Bulletin of the American Mathematical Society Suitable for advanced undergraduate and graduate students of mathematics, this enduringly relevant text introduces the main basic principles that govern the theory of Lie groups. The treatment opens with an overview of the classical linear groups and of topological groups, focusing on the theory of covering spaces and groups, which is developed independently from the theory of paths. Succeeding chapters contain an examination of the theory of analytic manifolds as well as a combination of the notions of topological group and manifold that defines analytic and Lie groups. An exposition of the differential calculus of Cartan follows and concludes with an exploration of compact Lie groups and their representations. |
Table des matières
| 1 | |
TopologICAL GROUPs | 25 |
MANIFolds | 68 |
ANALYTIC GROUPS LIE GROUPs | 99 |
W THE DIFFERENTIAL CALCULUs of CARTAN | 139 |
CoMPACT LIE GROUPS AND THEIR REPRESENTATIONS | 171 |
Autres éditions - Tout afficher
Theory of Lie Groups: Vol. 1 Claude Chevalley (Mathematiker, Frankreich) Aucun aperçu disponible - 1999 |
Expressions et termes fréquents
analytic group analytic infinitesimal transformation analytic isomorphism analytic subgroup assume automorphism belongs coefficients compact Lie group component contains continuous function coordinate system corresponds coset countability covering space cubic neighbourhood defined and analytic denote differential form dimension evenly covered fact finite number follows immediately form a system formula function f GL(n group G Hence hermitian matrix homomorphism identity mapping infinitesimal transformation integral manifold irreducible representation Lemma Let f Let G Let Q Lie algebra linear mapping locally connected matrices of degree modulo Moreover morphism neutral element open set open subset orthogonal Poincaré group proved Proposition proves our assertion quaternion real numbers representation space representative ring respect satisfies set of points simply connected covering SL(n ſº SO(n Sp(n SU(n system of coordinates tangent space tangent vector Theorem thereby proved topological group topological space underlying space unit matrix unitary univalent vector space whence