Non-Commutative Harmonic Analysis (Lecture Notes in Mathematics, v. 466)
Introduction to Liaison Theory and Deficiency Modules (Progress in Mathematics, #165)
by Juan C. Migliore
In the fall of 1992 I was invited by Professor Changho Keem to visit Seoul National University and give a series of talks. I was asked to write a monograph based on my talks, and the result was published by the Global Analysis Research Center of that University in 1994. The monograph treated deficiency modules and liaison theory for complete intersections. Over the next several years I continually thought of improvements and additions that I would like to make to the manuscript, and at the same...
Finite Groups (Surveys of Modern Mathematics)
Finite group theory is remarkable for the simplicity of its statements- and the difficulty of their proofs. It is essential in several branches of mathematics, notably number theory. Finite Groups: An Introduction is an elementary textbook on finite group theory. Written by the eminent French mathematician Jean-Pierre Serre (a principle contributor to algebraic geometry, group theory and number theory), this brand-new textbook is based upon a course given by Serrs st I'Ecole Normale Superieure...
Computational and Experimental Group Theory (Contemporary Mathematics)
Since its origin in the early 20th century, combinatorial group theory has been primarily concerned with algorithms for solving particular problems on groups given by generators and relations: word problems, conjugacy problems, isomorphism problems, etc. Recent years have seen the focus of algorithmic group theory shift from the decidability/undecidability type of result to the complexity of algorithms. Papers in this volume reflect that paradigm shift. Articles are based on the AMS/ASL Joint Sp...
Relatively Hyperbolic Groups (Memoirs of the American Mathematical Society)
by Denis V. Osin
In this paper we obtain an isoperimetric characterization of relatively hyperbolicity of a groups with respect to a collection of subgroups. This allows us to apply classical combinatorial methods related to van Kampen diagrams to obtain relative analogues of some well-known algebraic and geometric properties of ordinary hyperbolic groups. We also introduce and study the notion of a relatively quasi-convex subgroup of a relatively hyperbolic group and solve some natural algorithmic problems.
An Introduction to Quasigroups and Their Representations (Studies in Advanced Mathematics)
by Jonathan D. H. Smith
Collecting results scattered throughout the literature into one source, An Introduction to Quasigroups and Their Representations shows how representation theories for groups are capable of extending to general quasigroups and illustrates the added depth and richness that result from this extension. To fully understand representation theory, the first three chapters provide a foundation in the theory of quasigroups and loops, covering special classes, the combinatorial multiplication group, univ...
Nato dai corsi universitari di Teoria dei Gruppi tenuti per vari anni dall'autore, questo libro affronta gli argomenti fondamentali della teoria: gruppi abeliani, nilpotenti e risolubili, gruppi liberi, permutazioni, rappresentazioni e coomologia. Dopo le prime nozioni, viene esposto il programma di Hoelder per la classificazione dei gruppi finiti. Un lungo capitolo e dedicato all'azione di un gruppo su un insieme e alle permutazioni, sia sotto l'aspetto algebrico che combinatorio, con richiami...
Analysis on Lie Groups with Polynomial Growth (Progress in Mathematics, #214)
by Nick Dungey, A.F.M. (Tom) ter Elst, and Derek William Robinson
Analysis on Lie Groups with Polynomial Growth is the first book to present a method for examining the surprising connection between invariant differential operators and almost periodic operators on a suitable nilpotent Lie group. It deals with the theory of second-order, right invariant, elliptic operators on a large class of manifolds: Lie groups with polynomial growth. In systematically developing the analytic and algebraic background on Lie groups with polynomial growth, it is possible to des...
Wavelets Through a Looking Glass (Applied and Numerical Harmonic Analysis)
by Ola Bratteli and Palle Jorgensen
? Concise background material for each chapter, open problems, exercises, bibliography, and comprehensive index make this work a fine pedagogical and reference resource.; New previously unpublished results appear on the homotopy of multiresolutions, approximation theory, the spectrum and structure of the fixed points of the associated transfer, subdivision operators; Key topics of wavelet theory are examined; Excellent graphics show how wavelets depend on the spectra of the transfer operators; T...
Quantum Stochastic Calculus and Representations of Lie Superalgebras (Lecture Notes in Mathematics, #1692)
by Timothy M.W. Eyre
This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum stochastic calculus. Quantum stochastic calculus and grading theory are given concise introductions, extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite-dimensional Hilbert spaces. The develpment of an explicit formula for the chaotic expansion of a polynomial of quantum stochastic integrals is particularly interesting....
Periodic Locally Compact Groups (De Gruyter Studies in Mathematics)
by Wolfgang Herfort, Karl H. Hofmann, and Francesco G. Russo
This authoritative book on periodic locally compact groups is divided into three parts: The first part covers the necessary background material on locally compact groups including the Chabauty topology on the space of closed subgroups of a locally compact group, its Sylow theory, and the introduction, classifi cation and use of inductively monothetic groups. The second part develops a general structure theory of locally compact near abelian groups, pointing out some of its connections with nu...
In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra. This naive approach to Lie theory is originally due to von Neuma...
Classgroups and Hermitian Modules (Progress in Mathematics, #48)
by Albrecht Frohlich
These notes are an expanded and updated version of a course of lectures which I gave at King's College London during the summer term 1979. The main topic is the Hermitian classgroup of orders, and in particular of group rings. Most of this work is published here for the first time. The primary motivation came from the connection with the Galois module structure of rings of algebraic integers. The principal aim was to lay the theoretical basis for attacking what may be called the "converse proble...
Perfect Groups (Oxford Mathematical Monographs)
by Derek F. Holt and W. Plesken
The aim of this book is to provide a systematic source of examples of finite perfect groups. The constructions of perfect groups are discussed from two viewpoints: classifying finite perfect groups of small order, and using infinite perfect groups to construct infinite sequences of finite perfect factor groups. The first part of the book is theoretical, centering on the "graph of perfect groups". These constructions throw light on some interesting subgraphs and on asymptotic behaviour. The secon...
An Introduction to the Langlands Program
This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.
An Introduction to Quasigroups and Their Representations (Studies in Advanced Mathematics)
by Jonathan D Smith
Geometric Structures On 2-orbifolds (Mathematical Society Of Japan Memoirs, #27)
This book exposes the connection between the low-dimensional orbifold theory and geometry that was first discovered by Thurston in 1970s providing a key tool in his proof of the hyperbolization of Haken 3-manifolds. Our main aims are to explain most of the topology of orbifolds but to explain the geometric structure theory only for 2-dimensional orbifolds, including their Teichmuller (Fricke) spaces. We tried to collect the theory of orbifolds scattered in various literatures for our purposes. H...
Galois Theory of P-Extensions (Springer Monographs in Mathematics)
by Helmut Koch
Helmut Koch's classic is now available in English. Competently translated by Franz Lemmermeyer, it introduces the theory of pro-p groups and their cohomology. The book contains a postscript on the recent development of the field written by H. Koch and F. Lemmermeyer, along with many additional recent references.