Partially Ordered Abelian Groups With Interpolation
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Partially Ordered Abelian Groups With Interpolation
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Author : K. R. Goodearl
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-05-30
Partially Ordered Abelian Groups With Interpolation written by K. R. Goodearl 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 2010-05-30 with Mathematics categories.
A branch of ordered algebraic structures has grown, motivated by $K$-theoretic applications and mainly concerned with partially ordered abelian groups satisfying the Riesz interpolation property. This monograph is the first source in which the algebraic and analytic aspects of these interpolation groups have been integrated into a coherent framework for general reference. The author provides a solid foundation in the structure theory of interpolation groups and dimension groups (directed unperforated interpolation groups), with applications to ordered $K$-theory particularly in mind. Although interpolation groups are defined as purely algebraic structures, their development has been strongly influenced by functional analysis. This cross-cultural development has left interpolation groups somewhat estranged from both the algebraists, who may feel intimidated by compact convex sets, and the functional analysts, who may feel handicapped by the lack of scalars. This book, requiring only standard first-year graduate courses in algebra and functional analysis, aims to make the subject accessible to readers from both disciplines.High points of the development include the following: characterization of dimension groups as direct limits of finite products of copies of the integers; the double-dual representation of an interpolation group with order-unit via affine continuous real-valued functions on its state space; the structure of dimension groups complete with respect to the order-unit norm, as well as monotone sigma-complete dimension groups and dimension groups with countably infinite interpolation; and an introduction to the problem of classifying extensions of one dimension group by another. The book also includes a development of portions of the theory of compact convex sets and Choquet simplices, and an expository discussion of various applications of interpolation group theory to rings and $C DEGREES*$-algebras via ordered $K_0$. A discussion of some open problems in interpolation groups and dimension groups concludes the book.Of interest, of course, to researchers in ordered algebraic structures, the book will also be a valuable source for researchers seeking a background in interpolation groups and dimension groups for applications to such subjects as rings, operator algebras, topological Markov chains, positive polynomials, compact group actions, or other areas where ordered Grothendieck groups might be useful. This is a reprint of the 1986 original. (SUR
Partially Ordered Abelian Groups With Interpolation
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Author : K. P. Goodearl
language : en
Publisher:
Release Date : 1986
Partially Ordered Abelian Groups With Interpolation written by K. P. Goodearl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Affine Representations Of Grothendieck Groups And Applications To Rickart C Ast Algebras And Aleph 0 Continuous Regular Rings
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Author : K. R. Goodearl
language : en
Publisher: American Mathematical Soc.
Release Date : 1980
Affine Representations Of Grothendieck Groups And Applications To Rickart C Ast Algebras And Aleph 0 Continuous Regular Rings written by K. R. Goodearl 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 1980 with Mathematics categories.
This paper is concerned with the structure of three interrelated classes of objects: partially ordered abelian groups with countable interpolation, [Hebrew]Aleph0-continuous regular rings, and finite Rickart C*-algebras. The connection from these rings and algebras to these groups is the Grothendieck group K0, which, for all [Hebrew]Aleph0-continuous regular rings and most finite Rickart C*-algebras, is a partially ordered abelian group with countable interpolation. Such partially ordered groups are shown to possess quite specific representations in spaces of affine continuous functions on Choquet simplices. The theme of this paper is to develop the structure theory of these groups and these representations, and to translate the results, via K0, into properties of [Hebrew]Aleph0-continuous regular rings and finite Rickart C*-algebras.
Refinement Monoids Equidecomposability Types And Boolean Inverse Semigroups
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Author : Friedrich Wehrung
language : en
Publisher: Springer
Release Date : 2017-09-09
Refinement Monoids Equidecomposability Types And Boolean Inverse Semigroups written by Friedrich Wehrung and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-09 with Mathematics categories.
Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings. This is done via the study of a monoid invariant, defined on Boolean inverse semigroups, called the type monoid. The new techniques contrast with the currently available topological approaches. Many positive results, but also many counterexamples, are provided.
Commutative Semigroups
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Author : P.A. Grillet
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Commutative Semigroups written by P.A. Grillet 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 2013-06-29 with Mathematics categories.
This is the first book about commutative semigroups in general. Emphasis is on structure but the other parts of the theory are at least surveyed and a full set of about 850 references is included. The book is intended for mathematicians who do research on semigroups or who encounter commutative semigroups in their research.
Algebra And Its Applications
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Author : H. L. Manocha
language : en
Publisher: CRC Press
Release Date : 1984-05-31
Algebra And Its Applications written by H. L. Manocha and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-05-31 with Mathematics categories.
This volume unites more than fifty international mathematicians, spotlighting research that demonstrates the importance of algebra in science and engineering. Areas in algebra such as invariant theory, group representations, commutative algebra, and algebraic geometry are important factors in such subjects as quantum physics, computing, and data communications. The International Symposium on Algebra and Its Applications was organized by the Department of Mathematics of the Indian Institute of Technology, and held in New Delhi, India, December 21-25, 1981. This volume contains papers presented, and the editors wish to express their appreciation to all the authors for their submissions, and symposium participants for their enthusiasm.
Elliptic Boundary Value Problems In Domains With Point Singularities
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Author : Vladimir Kozlov
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Elliptic Boundary Value Problems In Domains With Point Singularities written by Vladimir Kozlov 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.
For graduate students and research mathematicians interested in partial differential equations and who have a basic knowledge of functional analysis. Restricted to boundary value problems formed by differential operators, avoiding the use of pseudo- differential operators. Concentrates on fundamental results such as estimates for solutions in different function spaces, the Fredholm property of the problem's operator, regularity assertions, and asymptotic formulas for the solutions of near singular points. Considers the solutions in Sobolev spaces of both positive and negative orders. Annotation copyrighted by Book News, Inc., Portland, OR
The Convenient Setting Of Global Analysis
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Author : Andreas Kriegl
language : en
Publisher: American Mathematical Society
Release Date : 2024-08-15
The Convenient Setting Of Global Analysis written by Andreas Kriegl 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 2024-08-15 with Mathematics categories.
This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Fr‚chet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups. Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.
Homeomorphisms In Analysis
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Author : Casper Goffman
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Homeomorphisms In Analysis written by Casper Goffman 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.
This work features the interplay of two main branches of mathematics: topology and real analysis. The material of the book is largely contained in the research publications of the authors and their students from the past 50 years. Parts of analysis are touched upon in a unique way, for example, Lebesgue measurability, Baire classes of functions, differentiability, C ]n and C ]*w functions, the Blumberg theorem, bounded variation in the sense of Cesari, and various theorems on Fourier series and generalized bounded variation of a function.
Current Research In Operational Quantum Logic
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Author : Bob Coecke
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Current Research In Operational Quantum Logic written by Bob Coecke 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 2013-06-29 with Science categories.
The present volume has its origins in a pair of informal workshops held at the Free University of Brussels, in June of 1998 and May of 1999, named "Current Research 1 in Operational Quantum Logic". These brought together mathematicians and physicists working in operational quantum logic and related areas, as well as a number of interested philosophers of science, for a rare opportunity to discuss recent developments in this field. After some discussion, it was decided that, rather than producing a volume of conference proceedings, we would try to organize the conferees to produce a set of comprehensive survey papers, which would not only report on recent developments in quantum logic, but also provide a tutorial overview of the subject suitable for an interested non-specialist audience. The resulting volume provides an overview of the concepts and methods used in current research in quantum logic, viewed both as a branch of mathemati cal physics and as an area of pure mathematics. The first half of the book is concerned with the algebraic side of the subject, and in particular the theory of orthomodular lattices and posets, effect algebras, etc. In the second half of the book, special attention is given to categorical methods and to connections with theoretical computer science. At the 1999 workshop, we were fortunate to hear three excellent lectures by David J. Foulis, represented here by two contributions. Dave's work, spanning 40 years, has helped to define, and continues to reshape, the field of quantum logic.