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:
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.”
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: A readable exposition of how Euclidean and other geometries can be distinguished using linear algebra and transformation groups.
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:
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:
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
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:
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:
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.
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.
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.
Download or read book Atlas of Finite Groups written by John Horton Conway and published by Oxford University Press. This book was released on 1985 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This atlas covers groups from the families of the classification of finite simple groups. Recently updated incorporating corrections
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,
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.
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 177 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.
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.
Download or read book Representation Theory of Finite Groups and Associative Algebras written by Charles W. Curtis and published by American Mathematical Soc.. This book was released on 2006 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to various aspects of the representation theory of finite groups. This book covers such topics as general non-commutative algebras, Frobenius algebras, representations over non-algebraically closed fields and fields of non-zero characteristic, and integral representations.
