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Author : Stephen M. Gagola
Publisher :
ISBN 13 :
Total Pages : 142 pages
Book Rating : 4.3/5 (129 download)
Download or read book Subloops of the Unit Octonions written by Stephen M. Gagola and published by . This book was released on 2005 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. I. Hall
Publisher : American Mathematical Soc.
ISBN 13 : 1470436221
Total Pages : 186 pages
Book Rating : 4.4/5 (74 download)
Download or read book Moufang Loops and Groups with Triality are Essentially the Same Thing written by J. I. Hall and published by American Mathematical Soc.. This book was released on 2019-09-05 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1925 Élie Cartan introduced the principal of triality specifically for the Lie groups of type D4, and in 1935 Ruth Moufang initiated the study of Moufang loops. The observation of the title in 1978 was made by Stephen Doro, who was in turn motivated by the work of George Glauberman from 1968. Here the author makes the statement precise in a categorical context. In fact the most obvious categories of Moufang loops and groups with triality are not equivalent, hence the need for the word “essentially.”
Author :
Publisher :
ISBN 13 :
Total Pages : 1208 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 1208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : American Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 718 pages
Book Rating : 4.E/5 ( download)
Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 2005 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Norman W. Johnson
Publisher : Cambridge University Press
ISBN 13 : 1108132677
Total Pages : 455 pages
Book Rating : 4.1/5 (81 download)
Download or read book Geometries and Transformations written by Norman W. Johnson and published by Cambridge University Press. This book was released on 2018-06-07 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Euclidean and other geometries are distinguished by the transformations that preserve their essential properties. Using linear algebra and transformation groups, this book provides a readable exposition of how these classical geometries are both differentiated and connected. Following Cayley and Klein, the book builds on projective and inversive geometry to construct 'linear' and 'circular' geometries, including classical real metric spaces like Euclidean, hyperbolic, elliptic, and spherical, as well as their unitary counterparts. The first part of the book deals with the foundations and general properties of the various kinds of geometries. The latter part studies discrete-geometric structures and their symmetries in various spaces. Written for graduate students, the book includes numerous exercises and covers both classical results and new research in the field. An understanding of analytic geometry, linear algebra, and elementary group theory is assumed.
Author :
Publisher :
ISBN 13 :
Total Pages : 848 pages
Book Rating : 4.F/5 ( download)
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2006 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John H. Conway
Publisher : CRC Press
ISBN 13 : 1439864187
Total Pages : 172 pages
Book Rating : 4.4/5 (398 download)
Download or read book On Quaternions and Octonions written by John H. Conway and published by CRC Press. This book was released on 2003-01-23 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less f
Author :
Publisher :
ISBN 13 :
Total Pages : 790 pages
Book Rating : 4.:/5 (7 download)
Download or read book CMUC written by and published by . This book was released on 2004 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kenneth W. Johnson
Publisher : Springer Nature
ISBN 13 : 3030283003
Total Pages : 384 pages
Book Rating : 4.0/5 (32 download)
Download or read book Group Matrices, Group Determinants and Representation Theory written by Kenneth W. Johnson and published by Springer Nature. This book was released on 2019-11-08 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book sets out an account of the tools which Frobenius used to discover representation theory for nonabelian groups and describes its modern applications. It provides a new viewpoint from which one can examine various aspects of representation theory and areas of application, such as probability theory and harmonic analysis. For example, the focal objects of this book, group matrices, can be thought of as a generalization of the circulant matrices which are behind many important algorithms in information science. The book is designed to appeal to several audiences, primarily mathematicians working either in group representation theory or in areas of mathematics where representation theory is involved. Parts of it may be used to introduce undergraduates to representation theory by studying the appealing pattern structure of group matrices. It is also intended to attract readers who are curious about ideas close to the heart of group representation theory, which do not usually appear in modern accounts, but which offer new perspectives.
Author : Péter Nagy
Publisher : Walter de Gruyter
ISBN 13 : 3110900580
Total Pages : 377 pages
Book Rating : 4.1/5 (19 download)
Download or read book Loops in Group Theory and Lie Theory written by Péter Nagy and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Orin Chein
Publisher : American Mathematical Soc.
ISBN 13 : 0821821970
Total Pages : 140 pages
Book Rating : 4.8/5 (218 download)
Download or read book Moufang Loops of Small Order written by Orin Chein and published by American Mathematical Soc.. This book was released on 1978 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, all nonassociative Moufang loops of order [less-than or equal to symbol] 63 are found, and their properties are investigated. Each of these loops is solvable, satisfies Lagrange's Theorem, has Sylow subloops, and is isomorphic to all of its loop isotopes. All of the loops in question contain normal subgroups of small index, and some general techniques of constructing such loops are discussed.
Author : Richard D. Schafer
Publisher : Courier Dover Publications
ISBN 13 : 0486164179
Total Pages : 176 pages
Book Rating : 4.4/5 (861 download)
Download or read book An Introduction to Nonassociative Algebras written by Richard D. Schafer and published by Courier Dover Publications. This book was released on 2017-11-15 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise graduate-level introductory study presents some of the important ideas and results in the theory of nonassociative algebras. Places particular emphasis on alternative and (commutative) Jordan algebras. 1966 edition.
Author : L. Sabinin
Publisher : Springer Science & Business Media
ISBN 13 : 9401144915
Total Pages : 263 pages
Book Rating : 4.4/5 (11 download)
Download or read book Smooth Quasigroups and Loops written by L. Sabinin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last twenty-five years quite remarkable relations between nonas sociative algebra and differential geometry have been discovered in our work. Such exotic structures of algebra as quasigroups and loops were obtained from purely geometric structures such as affinely connected spaces. The notion ofodule was introduced as a fundamental algebraic invariant of differential geometry. For any space with an affine connection loopuscular, odular and geoodular structures (partial smooth algebras of a special kind) were introduced and studied. As it happened, the natural geoodular structure of an affinely connected space al lows us to reconstruct this space in a unique way. Moreover, any smooth ab stractly given geoodular structure generates in a unique manner an affinely con nected space with the natural geoodular structure isomorphic to the initial one. The above said means that any affinely connected (in particular, Riemannian) space can be treated as a purely algebraic structure equipped with smoothness. Numerous habitual geometric properties may be expressed in the language of geoodular structures by means of algebraic identities, etc.. Our treatment has led us to the purely algebraic concept of affinely connected (in particular, Riemannian) spaces; for example, one can consider a discrete, or, even, finite space with affine connection (in the form ofgeoodular structure) which can be used in the old problem of discrete space-time in relativity, essential for the quantum space-time theory.
Author : Jonathan D. H. Smith
Publisher : John Wiley & Sons
ISBN 13 : 1118030834
Total Pages : 386 pages
Book Rating : 4.1/5 (18 download)
Download or read book Post-Modern Algebra written by Jonathan D. H. Smith and published by John Wiley & Sons. This book was released on 2011-09-30 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced algebra in the service of contemporary mathematicalresearch-- a unique introduction. This volume takes an altogether new approach to advanced algebra.Its intriguing title, inspired by the term postmodernism, denotes adeparture from van der Waerden's Modern Algebra--a book that hasdominated the field for nearly seventy years. Post-Modern Algebraoffers a truly up-to-date alternative to the standard approach,explaining topics from an applications-based perspective ratherthan by abstract principles alone. The book broadens the field ofstudy to include algebraic structures and methods used in currentand emerging mathematical research, and describes the powerful yetsubtle techniques of universal algebra and category theory.Classical algebraic areas of groups, rings, fields, and vectorspaces are bolstered by such topics as ordered sets, monoids,monoid actions, quasigroups, loops, lattices, Boolean algebras,categories, and Heyting algebras. The text features: * A clear and concise treatment at an introductory level, tested inuniversity courses. * A wealth of exercises illustrating concepts and their practicalapplication. * Effective techniques for solving research problems in the realworld. * Flexibility of presentation, making it easy to tailor material tospecific needs. * Help with elementary proofs and algebraic notations for studentsof varying abilities. Post-Modern Algebra is an excellent primary or supplementary textfor graduate-level algebra courses. It is also an extremely usefulresource for professionals and researchers in many areas who musttackle abstract, linear, or universal algebra in the course oftheir work.
Author : Nathan Jacobson
Publisher : American Mathematical Soc.
ISBN 13 : 082184640X
Total Pages : 464 pages
Book Rating : 4.8/5 (218 download)
Download or read book Structure and Representations of Jordan Algebras written by Nathan Jacobson and published by American Mathematical Soc.. This book was released on 1968-12-31 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Jordan algebras has played important roles behind the scenes of several areas of mathematics. Jacobson's book has long been the definitive treatment of the subject. It covers foundational material, structure theory, and representation theory for Jordan algebras. Of course, there are immediate connections with Lie algebras, which Jacobson details in Chapter 8. Of particular continuing interest is the discussion of exceptional Jordan algebras, which serve to explain the exceptional Lie algebras and Lie groups. Jordan algebras originally arose in the attempts by Jordan, von Neumann, and Wigner to formulate the foundations of quantum mechanics. They are still useful and important in modern mathematical physics, as well as in Lie theory, geometry, and certain areas of analysis.
Author : Jonathan D. H. Smith
Publisher : CRC Press
ISBN 13 : 1420010638
Total Pages : 353 pages
Book Rating : 4.4/5 (2 download)
Download or read book An Introduction to Quasigroups and Their Representations written by Jonathan D. H. Smith and published by CRC Press. This book was released on 2006-11-15 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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,
Author : Martin J. Rees
Publisher :
ISBN 13 : 9780743230995
Total Pages : 288 pages
Book Rating : 4.2/5 (39 download)
Download or read book Before the Beginning written by Martin J. Rees and published by . This book was released on 2002 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The experimental and theoretical successes of cosmology in recent years offer the most dramatic enlargement of our concept of the universe since astronomers first realised the Sun's true place among the stars. In this groundbreaking, thought-provoking and accessible book Professor Sir Martin Rees argues that our universe is just one element in an infinite ensemble, a cosmic archipelago where impassable barriers prohibit communication between the islands. Our 'home universe' is an exceptional member of this ensemble, however, not least because it contains creatures able to observe it and contemplate its nature, past and future. One of these is Rees himself: one of the most creative and original of contemporary scientists, and a wonderful guide to the mysteries of the cosmos.
