Download or read book Decomposition of Division Algebras Into Tensor Product of Cyclic Algebras written by Jean Bernard Nganou and published by . This book was released on 2009 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Value Functions on Simple Algebras and Associated Graded Rings written by Jean-Pierre Tignol and published by Springer. This book was released on 2015-04-03 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur's construction of non crossed products and Platonov's solution of the Tannaka-Artin problem. This study is particularly timely because it approaches the subject from the perspective of associated graded structures. This new approach has been developed by the authors in the last few years and has significantly clarified the theory. Various constructions of division algebras are obtained as applications of the theory, such as noncrossed products and indecomposable algebras. In addition, the use of valuation theory in reduced Whitehead group calculations (after Hazrat and Wadsworth) and in essential dimension computations (after Baek and Merkurjev) is showcased. The intended audience consists of graduate students and research mathematicians.
Download or read book Finite Dimensional Division Algebras over Fields written by Nathan Jacobson and published by Springer Science & Business Media. This book was released on 2009-12-09 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, the eminent algebraist, Nathan Jacobsen, concentrates on those algebras that have an involution. Although they appear in many contexts, these algebras first arose in the study of the so-called "multiplication algebras of Riemann matrices". Of particular interest are the Jordan algebras determined by such algebras, and thus their structure is discussed in detail. Two important concepts also dealt with are the universal enveloping algebras and the reduced norm. However, the largest part of the book is the fifth chapter, which focuses on involutorial simple algebras of finite dimension over a field.
Download or read book Finite Dimensional Algebras written by Yurj A. Drozd and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This English edition has an additional chapter "Elements of Homological Al gebra". Homological methods appear to be effective in many problems in the theory of algebras; we hope their inclusion makes this book more complete and self-contained as a textbook. We have also taken this occasion to correct several inaccuracies and errors in the original Russian edition. We should like to express our gratitude to V. Dlab who has not only metic ulously translated the text, but has also contributed by writing an Appendix devoted to a new important class of algebras, viz. quasi-hereditary algebras. Finally, we are indebted to the publishers, Springer-Verlag, for enabling this book to reach such a wide audience in the world of mathematical community. Kiev, February 1993 Yu.A. Drozd V.V. Kirichenko Preface The theory of finite dimensional algebras is one of the oldest branches of modern algebra. Its origin is linked to the work of Hamilton who discovered the famous algebra of quaternions, and Cayley who developed matrix theory. Later finite dimensional algebras were studied by a large number of mathematicians including B. Peirce, C.S. Peirce, Clifford, ·Weierstrass, Dedekind, Jordan and Frobenius. At the end of the last century T. Molien and E. Cartan described the semisimple algebras over the complex and real fields and paved the first steps towards the study of non-semi simple algebras.
Download or read book Lectures on Division Algebras written by David J. Saltman and published by American Mathematical Soc.. This book was released on with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on lectures on division algebras given at a conference held at Colorado State University. Although division algebras are a very classical object, this book presents this "classical" material in a new way, highlighting current approaches and new theorems, and illuminating the connections with a variety of areas in mathematics.
Download or read book Valuation Theory and Its Applications written by Franz-Viktor Kuhlmann and published by American Mathematical Soc.. This book was released on 2002-01-01 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first of two proceedings volumes stemming from the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan (Saskatoon, SK, Canada). Valuation theory arose in the early part of the twentieth century in connection with number theory and has many important applications to geometry and analysis: the classical application to the study of algebraic curves and to Dedekind and Prufer domains; the close connection to the famousresolution of the singularities problem; the study of the absolute Galois group of a field; the connection between ordering, valuations, and quadratic forms over a formally real field; the application to real algebraic geometry; the study of noncommutative rings; etc. The special feature of this book isits focus on current applications of valuation theory to this broad range of topics. Also included is a paper on the history of valuation theory. The book is suitable for graduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic.
Download or read book Algebra IX written by A.I. Kostrikin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first contribution by Carter covers the theory of finite groups of Lie type, an important field of current mathematical research. In the second part, Platonov and Yanchevskii survey the structure of finite-dimensional division algebras, including an account of reduced K-theory.
Download or read book Decomposability of Tensors written by Luca Chiantini and published by MDPI. This book was released on 2019-02-15 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Decomposability of Tensors" that was published in Mathematics
Download or read book An Introduction to Central Simple Algebras and Their Applications to Wireless Communication written by Grégory Berhuy and published by American Mathematical Soc.. This book was released on 2013-07-05 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Central simple algebras arise naturally in many areas of mathematics. They are closely connected with ring theory, but are also important in representation theory, algebraic geometry and number theory. Recently, surprising applications of the theory of central simple algebras have arisen in the context of coding for wireless communication. The exposition in the book takes advantage of this serendipity, presenting an introduction to the theory of central simple algebras intertwined with its applications to coding theory. Many results or constructions from the standard theory are presented in classical form, but with a focus on explicit techniques and examples, often from coding theory. Topics covered include quaternion algebras, splitting fields, the Skolem-Noether Theorem, the Brauer group, crossed products, cyclic algebras and algebras with a unitary involution. Code constructions give the opportunity for many examples and explicit computations. This book provides an introduction to the theory of central algebras accessible to graduate students, while also presenting topics in coding theory for wireless communication for a mathematical audience. It is also suitable for coding theorists interested in learning how division algebras may be useful for coding in wireless communication.
Download or read book Division Algebras Over Generalized Local Fields written by Frank Hung-Yueh Chang and published by . This book was released on 2004 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quaternion Algebras written by John Voight and published by Springer Nature. This book was released on 2021-06-28 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.
Download or read book Issues in Algebra Geometry and Topology 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Algebra, Geometry, and Topology / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Topology. The editors have built Issues in Algebra, Geometry, and Topology: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Topology in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Algebra, Geometry, and Topology: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Download or read book Maximal nilpotent subalgebras I Nilradicals and Cartan subalgebras in associative algebras With 428 exercises written by Sven Bodo Wirsing and published by diplom.de. This book was released on 2016-12-08 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the author’s doctorate time at the Christian-Albrechts-Universitat to Kiel, Salvatore Siciliano gave a stimulating talk in the upper seminar algebra theory about Cartan subalgebras in Lie algebra associates to associative algebra. This talk was the incentive for the author to analyze maximal nilpotent substructures of the Lie algebra associated to associative algebras. In the present work Siciliano's theory about Cartan subalgebras is worked off and expanded to different special associative algebra classes. In addition, a second maximal nilpotent substructure is analyzed: the nilradical. Within this analysis the main focus is to describe these substructure with the associative structure of the underlying algebra. This is successfully realized in this work. Numerous examples (like group algebras and Solomon (Tits-) algebras) illustrate the results to the reader. Within the numerous exercises these results can be applied by the reader to get a deeper insight in this theory.
Download or read book Tensor Spaces and Exterior Algebra written by Takeo Yokonuma and published by American Mathematical Soc.. This book was released on 1992 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. to facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. in particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.
Download or read book Central Simple Algebras and Galois Cohomology written by Philippe Gille and published by Cambridge University Press. This book was released on 2017-08-10 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive modern introduction to central simple algebra starting from the basics and reaching advanced results.
Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tensor Algebra and Tensor Analysis for Engineers written by Mikhail Itskov and published by Springer Science & Business Media. This book was released on 2009-04-30 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a large gap between engineering courses in tensor algebra on one hand, and the treatment of linear transformations within classical linear algebra on the other. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling autonomous study. The last chapters deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.
