Exponential Groups
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The Geometry Of Infinite Dimensional Groups
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Author : Boris Khesin
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-28
The Geometry Of Infinite Dimensional Groups written by Boris Khesin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-28 with Mathematics categories.
This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.
Lie Groups And Subsemigroups With Surjective Exponential Function
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Author : Karl Heinrich Hofmann
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Lie Groups And Subsemigroups With Surjective Exponential Function written by Karl Heinrich Hofmann and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
In the structure theory of real Lie groups, there is still information lacking about the exponential function. Most notably, there are no general necessary and sufficient conditions for the exponential function to be surjective. It is surprising that for subsemigroups of Lie groups, the question of the surjectivity of the exponential function can be answered. Under nature reductions setting aside the "group part" of the problem, subsemigroups of Lie groups with surjective exponential function are completely classified and explicitly constructed in this memoir. There are fewer than one would think and the proofs are harder than one would expect, requiring some innovative twists. The main protagonists on the scene are SL(2, R) and its universal covering group, almost abelian solvable Lie groups (ie. vector groups extended by homotheties), and compact Lie groups. This text will also be of interest to those working in algebra and algebraic geometry.
Exponential Genus Problems In One Relator Products Of Groups
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Author : Andrew James Duncan
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Exponential Genus Problems In One Relator Products Of Groups written by Andrew James Duncan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Business & Economics categories.
Exponential equations in free groups were studied initially by Lyndon and Schutzenberger and then by Comerford and Edmunds. Comerford and Edmunds showed that the problem of determining whether or not the class of quadratic exponential equations have solution is decidable, in finitely generated free groups. In this paper the author shows that for finite systems of quadratic exponential equations decidability passes, under certain hypotheses, from the factor groups to free products and one-relator products.
The Elementary Theory Of Groups
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Author : Benjamin Fine
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-10-29
The Elementary Theory Of Groups written by Benjamin Fine and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-29 with Mathematics categories.
After being an open question for sixty years the Tarski conjecture was answered in the affirmative by Olga Kharlampovich and Alexei Myasnikov and independently by Zlil Sela. Both proofs involve long and complicated applications of algebraic geometry over free groups as well as an extension of methods to solve equations in free groups originally developed by Razborov. This book is an examination of the material on the general elementary theory of groups that is necessary to begin to understand the proofs. This material includes a complete exposition of the theory of fully residually free groups or limit groups as well a complete description of the algebraic geometry of free groups. Also included are introductory material on combinatorial and geometric group theory and first-order logic. There is then a short outline of the proof of the Tarski conjectures in the manner of Kharlampovich and Myasnikov.
Groups Languages Algorithms
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Author : Alexandre Borovik
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Groups Languages Algorithms written by Alexandre Borovik and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Since the pioneering works of Novikov and Maltsev, group theory has been a testing ground for mathematical logic in its many manifestations, from the theory of algorithms to model theory. The interaction between logic and group theory led to many prominent results which enriched both disciplines. This volume reflects the major themes of the American Mathematical Society/Association for Symbolic Logic Joint Special Session (Baltimore, MD), Interactions between Logic, Group Theory and Computer Science. Included are papers devoted to the development of techniques used for the interaction of group theory and logic. It is suitable for graduate students and researchers interested in algorithmic and combinatorial group theory. A complement to this work is Volume 349 in the AMS series, Contemporary Mathematics, Computational and Experimental Group Theory, which arose from the same meeting and concentrates on the interaction of group theory and computer science.
Algebraic Groups And Lie Groups
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Author : Gus Lehrer
language : en
Publisher: Cambridge University Press
Release Date : 1997-01-23
Algebraic Groups And Lie Groups written by Gus Lehrer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-23 with Mathematics categories.
This volume contains original research articles by many of the world's leading researchers in algebraic and Lie groups. Its inclination is algebraic and geometic, although analytical aspects are included. The central theme reflects the interests of R. W. Richardson, viz connections between representation theory and the structure and geometry of algebraic groups. All workers on algebraic and Lie groups will find that this book contains a wealth of interesting material.
Matrix Groups
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Author : Andrew Baker
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-08-20
Matrix Groups written by Andrew Baker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-20 with Mathematics categories.
This book offers a first taste of the theory of Lie groups, focusing mainly on matrix groups: closed subgroups of real and complex general linear groups. The first part studies examples and describes classical families of simply connected compact groups. The second section introduces the idea of a lie group and explores the associated notion of a homogeneous space using orbits of smooth actions. The emphasis throughout is on accessibility.
Groups Graphs And Random Walks
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Author : Tullio Ceccherini-Silberstein
language : en
Publisher: Cambridge University Press
Release Date : 2017-06-29
Groups Graphs And Random Walks written by Tullio Ceccherini-Silberstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-29 with Mathematics categories.
An up-to-date, panoramic account of the theory of random walks on groups and graphs, outlining connections with various mathematical fields.
Groups And Topological Dynamics
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Author : Volodymyr Nekrashevych
language : en
Publisher: American Mathematical Society
Release Date : 2022-10-11
Groups And Topological Dynamics written by Volodymyr Nekrashevych and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-11 with Mathematics categories.
This book is devoted to group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using group theory to study symbolic dynamics, and other connections between group theory and dynamical systems. One of the main applications of this approach to group theory is the study of asymptotic properties of groups such as growth and amenability. The book presents recently developed techniques of studying groups of dynamical origin using the structure of their orbits and associated groupoids of germs, applications of the iterated monodromy groups to hyperbolic dynamical systems, topological full groups and their properties, amenable groups, groups of intermediate growth, and other topics. The book is suitable for graduate students and researchers interested in group theory, transformations defined by automata, topological and holomorphic dynamics, and theory of topological groupoids. Each chapter is supplemented by exercises of various levels of complexity.
Algorithmic Problems In Groups And Semigroups
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Author : Jean-Camille Birget
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algorithmic Problems In Groups And Semigroups written by Jean-Camille Birget and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume contains papers which are based primarily on talks given at an inter national conference on Algorithmic Problems in Groups and Semigroups held at the University of Nebraska-Lincoln from May ll-May 16, 1998. The conference coincided with the Centennial Celebration of the Department of Mathematics and Statistics at the University of Nebraska-Lincoln on the occasion of the one hun dredth anniversary of the granting of the first Ph.D. by the department. Funding was provided by the US National Science Foundation, the Department of Math ematics and Statistics, and the College of Arts and Sciences at the University of Nebraska-Lincoln, through the College's focus program in Discrete, Experimental and Applied Mathematics. The purpose of the conference was to bring together researchers with interests in algorithmic problems in group theory, semigroup theory and computer science. A particularly useful feature of this conference was that it provided a framework for exchange of ideas between the research communities in semigroup theory and group theory, and several of the papers collected here reflect this interac tion of ideas. The papers collected in this volume represent a cross section of some of the results and ideas that were discussed in the conference. They reflect a synthesis of overlapping ideas and techniques stimulated by problems concerning finite monoids, finitely presented mono ids, finitely presented groups and free groups.