Theory Of K Loops
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Author | : Hubert Kiechle |
Publisher | : Springer |
Total Pages | : 200 |
Release | : 2004-10-12 |
Genre | : Mathematics |
ISBN | : 3540458174 |
The book contains the first systematic exposition of the current known theory of K-loops, as well as some new material. In particular, big classes of examples are constructed. The theory for sharply 2-transitive groups is generalized to the theory of Frobenius groups with many involutions. A detailed discussion of the relativistic velocity addition based on the author's construction of K-loops from classical groups is also included. The first chapters of the book can be used as a text, the later chapters are research notes, and only partially suitable for the classroom. The style is concise, but complete proofs are given. The prerequisites are a basic knowledge of algebra such as groups, fields, and vector spaces with forms.
Author | : Péter T. Nagy |
Publisher | : Walter de Gruyter |
Total Pages | : 384 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9783110170108 |
In this book the theory of binary systems is considered as a part of group theory and, in particular, within the framework of Lie groups. The novelty is the consequent treatment of topological and differentiable loops as topological and differentiable sections in Lie groups. The interplay of methods and tools from group theory, differential geometry and topology, symmetric spaces, topological geometry, and the theory of foliations is what gives a special flavour to the results presented in this book. It is the first monograph devoted to the study of global loops. So far books on differentiable loops deal with local loops only. This theory can only be used partially for the theory of global loops since non-associative local structures have, in general, no global forms. The text is addressed to researchers in non-associative algebra and foundations of geometry. It should prove enlightening to a broad range of readers, including mathematicians working in group theory, the theory of Lie groups, in differential and topological geometry, and in algebraic groups. The authors have produced a text that is suitable not only for a graduate course, but also for selfstudy in the subjectby interested graduate students. Moreover, the material presented can be used for lectures and seminars in algebra, topological algebra and geometry.
Author | : Rodolfo Gambini |
Publisher | : Cambridge University Press |
Total Pages | : 341 |
Release | : 2023-01-31 |
Genre | : Science |
ISBN | : 1009290193 |
This volume provides a self-contained introduction to applications of loop representations in particle physics and quantum gravity, in order to explore the gauge invariant quantization of Yang-Mills theories and gravity. First published in 1996, this title has been reissued as an Open Access publication on Cambridge Core.
Author | : Francis Willoughby Clarke |
Publisher | : |
Total Pages | : 278 |
Release | : 1971 |
Genre | : |
ISBN | : |
Author | : J.W. Addison |
Publisher | : Elsevier |
Total Pages | : 513 |
Release | : 2014-05-27 |
Genre | : Mathematics |
ISBN | : 1483275345 |
Studies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis's systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders on Boolean notions extended to higher dimensions, elementary theories with models without automorphisms, and applications of the notions of forcing and generic sets. The manuscript takes a look at a hypothesis concerning the extension of finite relations and its verification for certain special cases, theories of functors and models, model-theoretic methods in the study of elementary logic, and extensions of relational structures. The text also reviews relatively categorical and normal theories, algebraic theories, categories, and functors, denumerable models of theories with extra predicates, and non-standard models for fragments of number theory. The selection is highly recommended for mathematicians and researchers interested in the theory of models.
Author | : Douglas R. Hofstadter |
Publisher | : Basic Books (AZ) |
Total Pages | : 537 |
Release | : 2007-03-27 |
Genre | : Science |
ISBN | : 0465030785 |
Argues that the key to understanding ourselves and consciousness is the "strange loop," a special kind of abstract feedback loop that inhabits the brain.
Author | : Angélica María Osorno |
Publisher | : |
Total Pages | : 64 |
Release | : 2010 |
Genre | : |
ISBN | : |
In recent work of Baas-Dundas-Richter-Rognes, the authors introduce the notion of the K- theory of a bimonoidal category R, and show that it is equivalent to the algebraic K-theory space of the ring spectrum KR. In this thesis we show that K(R) is the group completion of the classifying space of the 2-category ModR of modules over R, and show that ModR is a symmetric monoidal 2-category. We explain how to use this symmetric monoidal structure to produce a [Gamma]-(2-category), which gives an infinite loop space structure on K(R). We show that the equivalence mentioned above is an equivalence of infinite loop spaces.
Author | : Thomas Schuster |
Publisher | : Springer |
Total Pages | : 193 |
Release | : 2007-04-26 |
Genre | : Mathematics |
ISBN | : 3540712275 |
This book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings. It demonstrates the performance and functionality of the method on several examples from medical imaging and non-destructive testing, such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography.
Author | : J.P. May |
Publisher | : Springer |
Total Pages | : 184 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540376038 |
Author | : Koichi Yamawaki |
Publisher | : World Scientific |
Total Pages | : 439 |
Release | : 2008-01-09 |
Genre | : Science |
ISBN | : 9814475475 |
This volume includes discussion on new dynamical features in the light of (deconstruted/latticized) extra dimensions, holographic QCD, Moose/hidden local symmetry, and so on. New insights into the QCD as a prototype of strong coupling gauge theories as well as in its own right, particularly in hot and dense matter are included.