Spherical buildings are certain combinatorial simplicial complexes intro- duced, at first in the language of "e;incidence geometries,"e; to provide a sys- tematic geometric interpretation of the exceptional complex Lie groups.
This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curva- ture -1, which is traditionally called hyperbolic 3-space.
The finite simple groups are basic objects in algebra since many questions about general finite groups can be reduced to questions about the simple groups.
The problems being solved by invariant theory are far-reaching generalizations and extensions of problems on the "e;reduction to canonical form"e; of various is almost the same thing, projective geometry.
In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics.
Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.
Of all topological algebraic structures compact topological groups have perhaps the richest theory since 80 many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geo- metry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric structure of compact groups via limit spaces; global topology and the theory of manifolds again playa role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory.
Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics.
Eine gleichermaßen aktuelle wie zusammenfassende Darstellung der wichtigsten Methoden zur Untersuchung der klassischen Gruppen fehlte bislang in deutschsprachigen Lehrbüchern.
This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68.
The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the best-known example of a non-commutative alge- 1 bra * Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat- ics.
Analysis on Symmetric spaces, or more generally, on homogeneous spaces of semisimple Lie groups, is a subject that has undergone a vigorous development in recent years, and has become a central part of contemporary mathematics.
The modern theory of Kleinian groups starts with the work of Lars Ahlfors and Lipman Bers; specifically with Ahlfors' finiteness theorem, and Bers' observation that their joint work on the Beltrami equation has deep implications for the theory of Kleinian groups and their deformations.
This book is devoted to the theory of geometries which are locally Euclidean, in the sense that in small regions they are identical to the geometry of the Euclidean plane or Euclidean 3-space.
This is the sixth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research.
Assuming only basic algebra and Galois theory, the book develops the method of "e;algebraic patching"e; to realize finite groups and, more generally, to solve finite split embedding problems over fields.
One of the beautiful results in the representation theory of the finite groups is McKay's theorem on a correspondence between representations of the binary polyhedral group of SU(2) and vertices of an extended simply-laced Dynkin diagram.
The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus.
