Smooth Quasigroups and Loops

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Publisher : Springer Science & Business Media
ISBN 13 : 9401144915
Total Pages : 263 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Smooth Quasigroups and Loops by : L. Sabinin

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.

A Study of New Concepts in Smarandache Quasigroups and Loops

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Publisher : Infinite Study
ISBN 13 : 1599730839
Total Pages : 139 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis A Study of New Concepts in Smarandache Quasigroups and Loops by : Jaiyeola Temitope Gbolahan

Download or read book A Study of New Concepts in Smarandache Quasigroups and Loops written by Jaiyeola Temitope Gbolahan and published by Infinite Study. This book was released on 2009 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Group Matrices, Group Determinants and Representation Theory

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Publisher : Springer Nature
ISBN 13 : 3030283003
Total Pages : 400 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Group Matrices, Group Determinants and Representation Theory by : Kenneth W. Johnson

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 400 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.

Quasigroups and Loops

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Publisher :
ISBN 13 :
Total Pages : 596 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Quasigroups and Loops by : Orin Chein

Download or read book Quasigroups and Loops written by Orin Chein and published by . This book was released on 1990 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Index to Theses with Abstracts Accepted for Higher Degrees by the Universities of Great Britain and Ireland and the Council for National Academic Awards

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Publisher :
ISBN 13 :
Total Pages : 348 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Index to Theses with Abstracts Accepted for Higher Degrees by the Universities of Great Britain and Ireland and the Council for National Academic Awards by :

Download or read book Index to Theses with Abstracts Accepted for Higher Degrees by the Universities of Great Britain and Ireland and the Council for National Academic Awards written by and published by . This book was released on 2005 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonassociative Mathematics and its Applications

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Publisher : American Mathematical Soc.
ISBN 13 : 1470442450
Total Pages : 310 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Nonassociative Mathematics and its Applications by : Petr Vojtěchovský

Download or read book Nonassociative Mathematics and its Applications written by Petr Vojtěchovský and published by American Mathematical Soc.. This book was released on 2019-01-14 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonassociative mathematics is a broad research area that studies mathematical structures violating the associative law x(yz)=(xy)z. The topics covered by nonassociative mathematics include quasigroups, loops, Latin squares, Lie algebras, Jordan algebras, octonions, racks, quandles, and their applications. This volume contains the proceedings of the Fourth Mile High Conference on Nonassociative Mathematics, held from July 29–August 5, 2017, at the University of Denver, Denver, Colorado. Included are research papers covering active areas of investigation, survey papers covering Leibniz algebras, self-distributive structures, and rack homology, and a sampling of applications ranging from Yang-Mills theory to the Yang-Baxter equation and Laver tables. An important aspect of nonassociative mathematics is the wide range of methods employed, from purely algebraic to geometric, topological, and computational, including automated deduction, all of which play an important role in this book.

An Introduction to Quasigroups and Their Representations

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Publisher : CRC Press
ISBN 13 : 1420010638
Total Pages : 353 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis An Introduction to Quasigroups and Their Representations by : Jonathan D. H. Smith

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,

A Survey of Binary Systems

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Publisher : Springer
ISBN 13 : 366243119X
Total Pages : 195 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis A Survey of Binary Systems by : Richard Hubert Bruck

Download or read book A Survey of Binary Systems written by Richard Hubert Bruck and published by Springer. This book was released on 2013-12-11 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Non-Associative Algebra and Its Applications

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Publisher : CRC Press
ISBN 13 : 9780824726690
Total Pages : 558 pages
Book Rating : 4.7/5 (266 download)

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Book Synopsis Non-Associative Algebra and Its Applications by : Lev Sabinin

Download or read book Non-Associative Algebra and Its Applications written by Lev Sabinin and published by CRC Press. This book was released on 2006-01-13 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences. This book covers material such as Jordan superalgebras, nonassociative deformations, nonassociative generalization of Hopf algebras, the structure of free algebras, derivations of Lie algebras, and the identities of Albert algebra. It also includes applications of smooth quasigroups and loops to differential geometry and relativity.

Loops in Group Theory and Lie Theory

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Publisher : Walter de Gruyter
ISBN 13 : 3110900580
Total Pages : 377 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Loops in Group Theory and Lie Theory by : Péter Nagy

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.

Algebra without Borders – Classical and Constructive Nonassociative Algebraic Structures

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Publisher : Springer Nature
ISBN 13 : 3031393341
Total Pages : 600 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Algebra without Borders – Classical and Constructive Nonassociative Algebraic Structures by : Mahouton Norbert Hounkonnou

Download or read book Algebra without Borders – Classical and Constructive Nonassociative Algebraic Structures written by Mahouton Norbert Hounkonnou and published by Springer Nature. This book was released on 2023-12-01 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers invited, peer-reviewed works presented at the 2021 edition of the Classical and Constructive Nonassociative Algebraic Structures: Foundations and Applications—CaCNAS: FA 2021, virtually held from June 30 to July 2, 2021, in dedication to the memory of Professor Nebojša Stevanović (1962-2009). The papers cover new trends in the field, focusing on the growing development of applications in other disciplines. These aspects interplay in the same cadence, promoting interactions between theory and applications, and between nonassociative algebraic structures and various fields in pure and applied mathematics. In this volume, the reader will find novel studies on topics such as left almost algebras, logical algebras, groupoids and their generalizations, algebraic geometry and its relations with quiver algebras, enumerative combinatorics, representation theory, fuzzy logic and foundation theory, fuzzy algebraic structures, group amalgams, computer-aided development and transformation of the theory of nonassociative algebraic structures, and applications within natural sciences and engineering. Researchers and graduate students in algebraic structures and their applications can hugely benefit from this book, which can also interest any researcher exploring multi-disciplinarity and complexity in the scientific realm.

Elements of Quasigroup Theory and Applications

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Publisher : CRC Press
ISBN 13 : 1498721567
Total Pages : 599 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Elements of Quasigroup Theory and Applications by : Victor Shcherbacov

Download or read book Elements of Quasigroup Theory and Applications written by Victor Shcherbacov and published by CRC Press. This book was released on 2017-05-12 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding Interaction is a book that explores the interaction between people and technology, in the broader context of the relations between the human made and the natural environments. It is not just about digital technologies – our computers, smart phones, the Internet – but all our technologies such as mechanical, electrical and electronic. Our ancestors started creating mechanical tools and shaping their environments millions of years ago, developing cultures and languages, which in turn influenced our evolution. Volume 1 of Understanding Interaction looks into this deep history – starting from the tool creating period (the longest and most influential on our physical and mental capacities), to the settlement period (agriculture, domestication, villages and cities, written language), the industrial period (science, engineering, reformation and renaissance), and finally the communication period (mass media, digital technologies, global networks). Volume 2 looks into humans in interaction – our physiology, anatomy, neurology, psychology, how we experience and influence the world, and how we (think we) think. From this transdisciplinary understanding, design approaches and frameworks are presented, to potentially guide future developments and innovations. The aim of the book is to be guide and inspiration for designers, artists, engineers, psychologists, media producers, social scientists etc., and as such be useful for both novices and more experienced practitioners.

Universal Algebra, Algebraic Logic, and Databases

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Publisher : Springer Science & Business Media
ISBN 13 : 940110820X
Total Pages : 445 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Universal Algebra, Algebraic Logic, and Databases by : B. Plotkin

Download or read book Universal Algebra, Algebraic Logic, and Databases written by B. Plotkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern algebra, which not long ago seemed to be a science divorced from real life, now has numerous applications. Many fine algebraic structures are endowed with meaningful contents. Now and then practice suggests new and unexpected structures enriching algebra. This does not mean that algebra has become merely a tool for applications. Quite the contrary, it significantly benefits from the new connections. The present book is devoted to some algebraic aspects of the theory of databases. It consists of three parts. The first part contains information about universal algebra, algebraic logic is the subject of the second part, and the third one deals with databases. The algebraic material of the flI'St two parts serves the common purpose of applying algebra to databases. The book is intended for use by mathematicians, and mainly by algebraists, who realize the necessity to unite theory and practice. It is also addressed to programmers, engineers and all potential users of mathematics who want to construct their models with the help of algebra and logic. Nowadays, the majority of professional mathematicians work in close cooperation with representatives of applied sciences and even industrial technology. It is neces sary to develop an ability to see mathematics in different particular situations. One of the tasks of this book is to promote the acquisition of such skills.

Handbook of Differential Geometry, Volume 1

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Publisher : Elsevier
ISBN 13 : 0080532837
Total Pages : 1067 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Differential Geometry, Volume 1 by : F.J.E. Dillen

Download or read book Handbook of Differential Geometry, Volume 1 written by F.J.E. Dillen and published by Elsevier. This book was released on 1999-12-16 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.

Bulletin of the American Mathematical Society

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Publisher :
ISBN 13 :
Total Pages : 634 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Bulletin of the American Mathematical Society by : American Mathematical Society

Download or read book Bulletin of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1961 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Survey of Binary Systems

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Publisher : Springer
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis A Survey of Binary Systems by : Richard H. Bruck

Download or read book A Survey of Binary Systems written by Richard H. Bruck and published by Springer. This book was released on 1971 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 916 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt: