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 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 On the Characters of the Representations of Division Algebras Over a Local Field written by Mitchell Phillip Laks and published by . This book was released on 1984 with total page 142 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 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 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 Finite Dimensional Division Algebras Over a Field written by Mitsue Nakamura-Sundnas and published by . This book was released on 1987 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Basic Number Theory written by Andre Weil and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Itpzf}JlOV, li~oxov uoq>ZUJlCJ. 7:WV Al(JX., llpoj1. AE(Jj1. The first part of this volume is based on a course taught at Princeton University in 1961-62; at that time, an excellent set ofnotes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes. Then, among some old papers of mine, I accidentally came across a long-forgotten manuscript by ChevaIley, of pre-war vintage (forgotten, that is to say, both by me and by its author) which, to my taste at least, seemed to have aged very welt It contained abrief but essentially com plete account of the main features of c1assfield theory, both local and global; and it soon became obvious that the usefulness of the intended volume would be greatly enhanced if I inc1uded such a treatment of this topic. It had to be expanded, in accordance with my own plans, but its outline could be preserved without much change. In fact, I have adhered to it rather c10sely at some critical points.
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 Collected Mathematical Papers Associative algebras and Riemann matrices written by Abraham Adrian Albert and published by American Mathematical Soc.. This book was released on with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the collected works of A. Adrian Albert, a leading algebraist of the twentieth century. Albert made many important contributions to the theory of the Brauer group and central simple algeras, Riemann matrices, nonassociative algebras and other topics. Part 1 focuses on associative algebras and Riemann matrices part 2 on nonassociative algebras and miscellany. Because much of Albert's work remains of vital interest in contemporary research, this volume will interst mathematicians in a variety of areas.
Download or read book Algebraic Groups and Number Theory Volume 1 written by Vladimir Platonov and published by Cambridge University Press. This book was released on 2023-08-31 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new material covering more recent developments. Volume I begins with chapters covering background material on number theory, algebraic groups, and cohomology (both abelian and non-abelian), and then turns to algebraic groups over locally compact fields. The remaining two chapters provide a detailed treatment of arithmetic subgroups and reduction theory in both the real and adelic settings. Volume I includes new material on groups with bounded generation and abstract arithmetic groups. With minimal prerequisites and complete proofs given whenever possible, this book is suitable for self-study for graduate students wishing to learn the subject as well as a reference for researchers in number theory, algebraic geometry, and related areas.
Download or read book Algebraic Groups and Number Theory written by Vladimir Platonov and published by Cambridge University Press. This book was released on 2023-08-31 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.
Download or read book Introduction to Quadratic Forms over Fields written by Tsit-Yuen Lam and published by American Mathematical Soc.. This book was released on 2005 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new version of the author's prizewinning book, Algebraic Theory of Quadratic Forms (W. A. Benjamin, Inc., 1973), gives a modern and self-contained introduction to the theory of quadratic forms over fields of characteristic different from two. Starting with few prerequisites beyond linear algebra, the author charts an expert course from Witt's classical theory of quadratic forms, quaternion and Clifford algebras, Artin-Schreier theory of formally real fields, and structural theorems on Witt rings, to the theory of Pfister forms, function fields, and field invariants. These main developments are seamlessly interwoven with excursions into Brauer-Wall groups, local and global fields, trace forms, Galois theory, and elementary algebraic K-theory, to create a uniquely original treatment of quadratic form theory over fields. Two new chapters totaling more than 100 pages have been added to the earlier incarnation of this book to take into account some of the newer results and more recent viewpoints in the area. As is characteristic of this author's expository style, the presentation of the main material in this book is interspersed with a copious number of carefully chosen examples to illustrate the general theory. This feature, together with a rich stock of some 280 exercises for the thirteen chapters, greatly enhances the pedagogical value of this book, both as a graduate text and as a reference work for researchers in algebra, number theory, algebraic geometry, algebraic topology, and geometric topology.
Download or read book Representations of Lie Groups Kyoto Hiroshima 1986 written by K. Okamoto and published by Academic Press. This book was released on 2014-07-22 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representations of Lie Groups, Kyoto, Hiroshima, 1986 contains the proceedings of a symposium on "Analysis on Homogeneous Spaces and Representations of Lie Groups" held on September 1-6, 1986 in Japan. The symposium provided a forum for discussing Lie groups and covered topics ranging from geometric constructions of representations to the irreducibility of discrete series representations for semisimple symmetric spaces. A classification theory of prehomogeneous vector spaces is also described. Comprised of 22 chapters, this volume first considers the characteristic varieties of certain modules over the enveloping algebra of a semisimple Lie algebra, such as highest weight modules and primitive quotients. The reader is then introduced to multiplicity one theorems for generalized Gelfand-Graev representations of semisimple Lie groups and Whittaker models for the discrete series. Subsequent chapters focus on Lie algebra cohomology and holomorphic continuation of generalized Jacquet integrals; the generalized Geroch conjecture; algebraic structures on virtual characters of a semisimple Lie group; and fundamental groups of semisimple symmetric spaces. The book concludes with an analysis of the boundedness of certain unitarizable Harish-Chandra modules. This monograph will appeal to students, specialists, and researchers in the field of pure mathematics.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2004 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Representation Theory and Number Theory in Connection with the Local Langlands Conjecture written by Jürgen Ritter and published by American Mathematical Soc.. This book was released on 1989 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Langlands Program summarizes those parts of mathematical research belonging to the representation theory of reductive groups and to class field theory. These two topics are connected by the vision that, roughly speaking, the irreducible representations of the general linear group may well serve as parameters for the description of all number fields. In the local case, the base field is a given $p$-adic field $K$ and the extension theory of $K$ is seen as determined by the irreducible representations of the absolute Galois group $G_K$ of $K$. Great progress has been made in establishing correspondence between the supercuspidal representations of $GL(n,K)$ and those irreducible representations of $G_K$ whose degrees divide $n$. Despite these advances, no book or paper has presented the different methods used or even collected known results. This volume contains the proceedings of the conference ``Representation Theory and Number Theory in Connection with the Local Langlands Conjecture,'' held in December 1985 at the University of Augsburg. The program of the conference was divided into two parts: (i) the representation theory of local division algebras and local Galois groups, and the Langlands conjecture in the tame case; and (ii) new results, such as the case $n=p$, the matching theorem, principal orders, tame Deligne representations, classification of representations of $GL(n)$, and the numerical Langlands conjecture. The collection of papers in this volume provides an excellent account of the current state of the local Langlands Program.
Download or read book K Theory and Algebraic Geometry Connections with Quadratic Forms and Division Algebras written by Bill Jacob and published by American Mathematical Soc.. This book was released on 1995 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1 of two - also available in a two volume set.
