Smooth Quasigroups And Loops
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Smooth Quasigroups And Loops
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Author : L. Sabinin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Smooth Quasigroups And Loops written by L. Sabinin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Quasigroups And Loops
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Author : Orin Chein
language : en
Publisher:
Release Date : 1990
Quasigroups And Loops written by Orin Chein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Loops (Group theory). categories.
Geometry And Algebra Of Multidimensional Three Webs
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Author : M. Akivis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometry And Algebra Of Multidimensional Three Webs written by M. Akivis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This monograph, which is the first to be devoted to the geometry of multidimensional three-webs, presents the classical adn up-to-date results of the theory, and those parts of geometry and algebra which are closely connected with it. Many problems of the theory of smooth quasigroups and loops are considered. In addition to the general theory of webs, important classes of special webs are also studied. The volume contains eight chapters dealing with geometric and algebraic structures associated with three-webs, transversally geodesic and isoclinic three-webs, Bol and Moufang three-webs, closed G-structures, automorphisms of three-webs, the geometry of the fourth-order differential neighborhood of a multidimensional three-web, and d-webs of codimension r. The book concludes with some appendices and a comprehensive bibliography. This volume will be of particular interest to graduate students and researchers working in the areas of differential and algebraic geometry and algebra.
Non Associative Algebra And Its Applications
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Author : Lev Sabinin
language : en
Publisher: CRC Press
Release Date : 2006-01-13
Non Associative Algebra And Its Applications written by Lev Sabinin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-13 with Mathematics categories.
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.
Nonassociative Algebra And Its Applications
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Author : R. Costa
language : en
Publisher: CRC Press
Release Date : 2019-05-20
Nonassociative Algebra And Its Applications written by R. Costa and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-20 with Mathematics categories.
A collection of lectures presented at the Fourth International Conference on Nonassociative Algebra and its Applications, held in Sao Paulo, Brazil. Topics in algebra theory include alternative, Bernstein, Jordan, lie, and Malcev algebras and superalgebras. The volume presents applications to population genetics theory, physics, and more.
Scientific Legacy Of Professor Zbigniew Oziewicz Selected Papers From The International Conference Applied Category Theory Graph Operad Logic
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Author : Hilda Maria Colin Garcia
language : en
Publisher: World Scientific
Release Date : 2023-09-27
Scientific Legacy Of Professor Zbigniew Oziewicz Selected Papers From The International Conference Applied Category Theory Graph Operad Logic written by Hilda Maria Colin Garcia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-27 with Mathematics categories.
Dedicated to the memory of the late Professor Zbigniew Oziewicz from Universidad Nacional Autónoma de México, the book consists of papers on a wide variety of topics related to the work of Professor Oziewicz, which were presented at the special conference on Graph-Operads-Logic (GOL 2021), selected through peer review to promote his scientific legacy.Professor Oziewicz was a great enthusiast and supporter of category theory and its applications in physics, as well as in various areas of mathematics (topology, noncommutative geometry, etc.). In particular, he made significant contributions to the theory of Frobenius algebras, which now are becoming more important due to their connection with topological quantum field theories that are used in mathematical physics and in quantum topology. Professor Oziewicz was a great and very generous teacher, who immersed his students in the beautiful ideas of category theory as well as mathematical physics and computation. It was his idea to start a series of conferences under the title Graphs-Operads-Logic, most of them held in Mexico, with some of them in the USA, which were a great platform to discuss various ideas connected with category theory and its various applications, and to make friends with other scientists. Despite his passing, the GOL 2021 conference is included in this series to pay tribute to his many contributions to diverse areas of science.The book is laid out in twelve main topics where we can find relevant works from distinguished experts.
Elements Of Quasigroup Theory And Applications
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Author : Victor Shcherbacov
language : en
Publisher: CRC Press
Release Date : 2017-05-12
Elements Of Quasigroup Theory And Applications written by Victor Shcherbacov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-12 with Computers categories.
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.
Theory Of K Loops
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Author : Hubert Kiechle
language : en
Publisher: Springer
Release Date : 2004-10-12
Theory Of K Loops written by Hubert Kiechle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-12 with Mathematics categories.
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.
Loops In Group Theory And Lie Theory
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Author : Péter Nagy
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24
Loops In Group Theory And Lie Theory written by Péter Nagy and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.
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.
Webs And Quasigroups
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Author :
language : en
Publisher:
Release Date : 1991
Webs And Quasigroups written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Nets (Mathematics) categories.
Vol. for 1991- has papers presented at: Non-Linear Geometric Algebra-89-
