Groups and group theory

This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics.

This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1).

This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "e;Lie Theory and Its Applications in Physics"e;, held near Varna, Bulgaria, in June 2015.

This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics.

Modern mathematics has become an essential part of today's physicist's arsenal and this book covers several relevant such topics.

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.

This lecture note provides a tutorial review of non-Abelian discrete groups and presents applications to particle physics where discrete symmetries constitute an important principle for model building.

This second edition addresses the question of which finite groups occur as Galois groups over a given field.

When we began to consider the scope of this book, we envisaged a catalogue supplying at least one abstract definition for any finitely- generated group that the reader might propose.

It is a great satisfaction for a mathematician to witness the growth and expansion of a theory in which he has taken some part during its early years.

This book is based on several courses given by the authors since 1966.

The 1963 Gottingen notes of T.

Inverse Galois Theory is concerned with the question of which finite groups occur as Galois Groups over a given field.

About 60 years ago, R.

This book is a study of group theoretical properties of two dis- parate kinds, firstly finiteness conditions or generalizations of fini- teness and secondly generalizations of solubility or nilpotence.

This book takes a snapshot of the mathematical foundations of classical and quantum mechanics from a contemporary mathematical viewpoint.

This book introduces the most important and useful algebraic and topological techniques for studying and calculating the cohomology of finite groups.

First published in German in 1970 and translated into Russian in 1973, this classic now becomes available in English.

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.

Part I of this book is a short review of the classical part of representation theory.

Spaces of constant curvature, i.

Group theory is one of the most fundamental branches ofmathematics.

This volume is the first in the series devoted to the commutative harmonic analysis, a fundamental part of the contemporary mathematics.

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.

The history of applications of space group theory to solid state physics goes back more than five decades.

The study of the structure of Lie algebras over arbitrary fields is now a little more than thirty years old.

Varieties of algebras are equationally defined classes of algebras, or "e;primitive classes"e; in MAL'CEV'S terminology.

By a linear group we mean essentially a group of invertible matrices with entries in some commutative field.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.

Der Autor wurde am 2.

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.

This book presents a comprehensive collection of integrals of the Fourier transformation type.

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.

Perhaps it is not inappropriate for me to begin with the comment that this book has been an interesting challenge to the translator.

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.