Quasigroups and Loops
Author | : Hala O. Pflugfelder |
Publisher | : |
Total Pages | : 172 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : |
Download Quasigroups and Loops Book in PDF, ePub and Kindle
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Quasigroups And Loops PDF full book. Access full book title Quasigroups And Loops.
Author | : Hala O. Pflugfelder |
Publisher | : |
Total Pages | : 172 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : |
Author | : Orin Chein |
Publisher | : |
Total Pages | : 596 |
Release | : 1990 |
Genre | : Loops (Group theory). |
ISBN | : |
Author | : L. Sabinin |
Publisher | : Springer Science & Business Media |
Total Pages | : 263 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401144915 |
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 | : CRC Press |
Total Pages | : 353 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 1420010638 |
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 | : Jaiyeola Temitope Gbolahan |
Publisher | : Infinite Study |
Total Pages | : 139 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 1599730839 |
This monograph is a compilation of results on some new Smarandache concepts in Smarandache;groupoids, quasigroups and loops, and it pin points the inter-relationships and connections between andamong the various Smarandache concepts and notions that have been developed. This monograph isstructured into six chapters. The first chapter is an introduction to the theory quasigroups and loops withmuch attention paid to those quasigroup and loop concepts whose Smarandache versions are to bestudied in the other chapters. In chapter two, the holomorphic structures of Smarandache loops ofBol-Moufang type and Smarandache loops of non-Bol-Moufang type are studied. In the third chapter,the notion of parastrophy is introduced into Smarandache quasigroups and studied. Chapter four studiesthe universality of some Smarandache loops of Bol-Moufang type. In chapter five, the notion ofSmarandache isotopism is introduced and studied in Smarandache quasigroups and loops. In chaptersix, by introducing Smarandache special mappings in Smarandache groupoids, the SmarandacheBryant-Schneider group of a Smarandache loop is developed.
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 | : J. I. Hall |
Publisher | : American Mathematical Soc. |
Total Pages | : 186 |
Release | : 2019-09-05 |
Genre | : Categories (Mathematics) |
ISBN | : 1470436221 |
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 | : Victor Shcherbacov |
Publisher | : CRC Press |
Total Pages | : 423 |
Release | : 2017-05-12 |
Genre | : Computers |
ISBN | : 1351646362 |
This book provides an introduction to quasigroup theory along with new structural results on some of the quasigroup classes. Many results are presented with some of them from mathematicians of the former USSR. These included results have not been published before in the western mathematical literature. In addition, many of the achievements obtained with regard to applications of quasigroups in coding theory and cryptology are described.
Author | : Phillip Alan Hartman |
Publisher | : |
Total Pages | : 124 |
Release | : 1971 |
Genre | : Group theory |
ISBN | : |
Author | : Tim Hardcastle |
Publisher | : |
Total Pages | : |
Release | : 2003 |
Genre | : |
ISBN | : |