الصفحة 1
الصفحة 1
Noetherian Semigroup Algebras
This work presents a comprehensive treatment of the main results and methods of the theory of Noetherian semigroup algebras. These general results are then applied and illustrated in the context of important classes of algebras that arise in a variety of areas and have been recently intensively studied. Several concrete constructions are described in full detail, in particular intriguing classes of quadratic algebras and algebras related to group rings of polycyclic-by-finite groups. These give new classes of Noetherian algebras of small Gelfand-Kirillov dimension. The focus is on the interplay between their combinatorics and the algebraic structure.
Nearrings and Nearfields ; Proceedings of the Conference on Nearrings and Nearfields, Hamburg, Germany July 27 - August 3, 2003
This present volume is the Proceedings of the 18th International Conference on Nearrings and Nearfields held at the Helmut-Schmidt-Universitat, Universitat der Bundeswehr Hamburg, from July 27-August 3, 2003. It contains the written versions of the lectures by the five invited speakers. These concern recent developments of planar nearrings, nearrings of mappings, group nearrings and loop-nearrings. One of them is a long and very substantial research paper "The Z-Constrained Conjecture". These are followed by 13 contributions reflecting the diversity of the subject of nearrings and related structures. Besides the purely algebriac structure theory, these papers show many connections of nearring theory with group theory, combinatorics, geometries, and topology, and all contain original research.
Metodi Matematici della Fisica = Mathematical Methods of Physics
This text draws its origin from my old notes, prepared for the course of Mathematical Methods of Physics and gradually arranged, refined and updated over the course of many years of teaching. The aim has always been to provide as simple and direct a presentation as possible of the mathematical methods relevant to Physics: Fourier series, Hilbert spaces, linear operators, functions of complex variables, Fourier and Laplace transforms, distributions. In addition to these basic topics, a brief introduction to the first notions of group theory, Lie algebras and symmetries in view of their applications to Physics is presented in the Appendix.
Mathematical Survey Lectures 1943-2004
This collection traces the career of Beno Eckmann, whose work ranges across a broad spectrum of mathematical concepts from topology and differential geometry through homological algebra to group theory. One of our most influential living mathematicians, Eckmann has been associated for nearly his entire professional life with the Swiss Federal Institute of Technology Zurich (ETH), as student, lecturer, professor, and professor emeritus.
Intégration : Chapitres 7 et 8 = Integration : Chapters 7 and 8
Nicolas BOURBAKI's Elements of Mathematics aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. applications. The concepts introduced, such as Haar measures and the convolution product, are the basis of harmonic analysis. It includes the chapters: Haar measure; Convolution and representations.
Infinite groups : geometric, combinatorial and dynamical aspects
This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics addressed in the book include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics, such as dynamical systems, geometry, operator algebras, probability theory, and others.
Gruppi : Una introduzione a idee e metodi della Teoria dei Gruppi = Groups : An introduction to the ideas and methods of Group Theory
Born from the university courses of Group Theory held by the author for several years, this book deals with the fundamental arguments of the theory: abelian, nilpotent and solvable groups, free groups, permutations, representations and cohomology. After the first notions, Hölder's program for the classification of finite groups is exposed. A long chapter is dedicated to the action of a group on a set and to the permutations, both under the algebraic and combinatorial aspects, with references to the theory of equations. Some questions of a logical nature are also considered, such as the decidability of the word problem for certain classes of groups. An essential aspect of the book is the presence of a great variety of exercises, about 400, mostly solved.
Group-based Cryptography
This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It is explored how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. It is also shown that there is a remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research avenues within group theory.
Group theory : Application to the physics of condensed matter
Every process in physics is governed by selection rules that are the consequence of symmetry requirements. The beauty and strength of group theory resides in the transformation of many complex symmetry operations into a very simple linear algebra. This concise and class-tested book has been pedagogically tailored over 30 years MIT and 2 years at the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory in close connection with applications helps students to learn, understand and use it for their own needs. For this reason, the theoretical background is confined to the first 4 introductory chapters (6-8 classroom hours). From there, each chapter develops new theory while introducing applications so that the students can best retain new concepts, build on concepts learned the previous week, and see interrelations between topics as presented.
Geometry and Dynamics of Groups and Spaces : In Memory of Alexander Reznikov
Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.
Geometric Group Theory ; Geneva and Barcelona Conferences
This volume assembles research papers in geometric and combinatorial group theory. This wide area may be defined as the study of those groups that are defined by their action on a combinatorial or geometric object, in the spirit of Klein’s programme.The contributions range over a wide spectrum: limit groups, groups associated with equations, with cellular automata, their structure as metric objects, their decomposition, etc. Their common denominator is the language of group theory, used to express and solve problems ranging from geometry to logic.
Geometric Fundamentals of Robotics
Geometric Fundamentals of Robotics provides an elegant introduction to the geometric concepts that are important to applications in robotics. This second edition is still unique in providing a deep understanding of the subject: rather than focusing on computational results in kinematics and robotics, it includes significant state-of-the art material that reflects important advances in the field, connecting robotics back to mathematical fundamentals in group theory and geometry.
Galois Theory
Classical Galois theory is a subject generally acknowledged to be one of the most central and beautiful areas in pure mathematics. This text develops the subject systematically and from the beginning, requiring of the reader only basic facts about polynomials and a good knowledge of linear algebra.The book discusses Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic extensions of the field of rational numbers. While most of the book is concerned with finite extensions, it concludes with a discussion of the algebraic closure and of infinite Galois extensions.
Fuzzy Group Theory
This book presents an up-to-date account of research in important topics of fuzzy group theory. The book concentrates on the theoretical aspects of fuzzy subgroups of a group. It also includes applications to some abstract recognition problems and to coding theory. The book begins with basic properties of fuzzy subgroups. The notions of ascending series and descending series of fuzzy subgroups are used to define nilpotency of a fuzzy subgroup. The material presented in this book makes it a good reference for graduate students and researchers working in fuzzy group theory.
From Geometry to quantum mechanics : In Honor of Hideki Omori
This volume is composed of invited expository articles by well-known mathematicians in differential geometry and mathematical physics that have been arranged in celebration of Hideki Omori's recent retirement from Tokyo University of Science and in honor of his fundamental contributions to these areas.The papers focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, infinite-dimensional Lie group theory, quantizations and noncommutative geometry, as well as applications of partial differential equations and variational methods to geometry.
Fields and Galois Theory
The pioneering work of Abel and Galois in the early nineteenth century demonstrated that the long-standing quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they used were, in the end, more important than the resolution of a somewhat esoteric problem, for they were the genesis of modern abstract algebra. This book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple - which is assuredly not the way Galois would have expressed the connection.
Evolution Algebras and their Applications
Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics.
Discovering Mathematics with Magma : Reducing the Abstract to the Concrete
This volume celebrates the first decade of the Computer Algebra system Magma. With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. The book range over much of Magma's coverage of algorithmic algebra: from number theory and algebraic geometry, via representation theory and group theory to some branches of discrete mathematics and graph theory. A basic introduction to the Magma language is given in an appendix. The book is simultaneously an invitation to learn a new programming language in the context of contemporary research problems, and an exposition of the types of problem that can be investigated using computational algebra.
Computational Noncommutative Algebra and Applications
The fusion of algebra, analysis and geometry, and their application to real world problems, have been dominant themes underlying mathematics for over the years. This book features topics such as: signal and image processing in remote sensing, computer vision, medical image processing, biological signal processing, geometric algebras, and more.
Combinatorics of Coxeter Groups
Coxeter groups are of central importance in several areas of algebra, geometry, and combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of Coxeter groups, such as reduced expressions, partial order of group elements, enumeration, associated graphs and combinatorial cell complexes, and connections with combinatorial representation theory. While Coxeter groups have already been exposited from algebraic and geometric perspectives, this text is the first one to focus mainly on the combinatorial aspects of Coxeter groups. The first part of the book provides a self-contained introduction to combinatorial Coxeter group theory. The emphasis here is on the combinatorics of reduced decompositions, Bruhat order, weak order, and some aspects of root systems. The second part deals with more advanced topics, such as Kazhdan-Lusztig polynomials and representations, enumeration, and combinatorial descriptions of the classical finite and affine Weyl groups. A wide variety of exercises, ranging from easy to quite difficult are also included.
