Logo Oapen
  • Search
  • Join
    • Deposit
    • For Librarians
    • For Publishers
    • For Researchers
    • Funders
    • Resources
    • OAPEN
    • For Librarians
    • For Publishers
    • For Researchers
    • Funders
    • Resources
    • OAPEN
    View Item 
    •   OAPEN Home
    • View Item
    •   OAPEN Home
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Quaternion Algebras

    Thumbnail
    Download PDF Viewer
    Web Shop
    Author(s)
    Voight, John
    Language
    English
    Show full item record
    Abstract
    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.
    URI
    https://library.oapen.org/handle/20.500.12657/50018
    Keywords
    Associative Rings and Algebras; Group Theory and Generalizations; Number Theory; Open Access; Quaternions; Quaternion algebras; Quaternion orders; Quaternion ideals; Noncommutative algebra; Quaternions and quadratic forms; Ternary quadratic forms; Simple algebras and involutions; Lattices and integral quadratic forms; Hurwitz order; Quaternion algebras over local fields; Quaternion algebras over global fields; Adelic framework; Idelic zeta functions; Quaternions hyperbolic geometry; Quaternions arithmetic groups; Quaternions arithmetic geometry; Supersingular elliptic curves; Abelian surfaces with QM; Algebra; Groups & group theory; Textbook
    DOI
    10.1007/978-3-030-56694-4
    ISBN
    9783030566944, 9783030566944
    Publisher
    Springer Nature
    Publisher website
    https://www.springernature.com/gp/products/books
    Publication date and place
    2021
    Grantor
    • Dartmouth College - [grantnumber unknown]
    Imprint
    Springer International Publishing
    Series
    Graduate Texts in Mathematics, 288
    Classification
    Algebra
    Groups and group theory
    Number theory
    Pages
    885
    Rights
    http://creativecommons.org/licenses/by-nc/4.0/
    • Imported or submitted locally

    Browse

    All of OAPENSubjectsPublishersLanguagesCollections

    My Account

    LoginRegister

    Export

    Repository metadata
    Logo Oapen
    • For Librarians
    • For Publishers
    • For Researchers
    • Funders
    • Resources
    • OAPEN

    Newsletter

    • Subscribe to our newsletter
    • view our news archive

    Follow us on

    License

    • If not noted otherwise all contents are available under Attribution 4.0 International (CC BY 4.0)

    Credits

    • logo EU
    • This project received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 683680, 810640, 871069 and 964352.

    OAPEN is based in the Netherlands, with its registered office in the National Library in The Hague.

    Director: Niels Stern

    Address:
    OAPEN Foundation
    Prins Willem-Alexanderhof 5
    2595 BE The Hague
    Postal address:
    OAPEN Foundation
    P.O. Box 90407
    2509 LK The Hague

    Websites:
    OAPEN Home: www.oapen.org
    OAPEN Library: library.oapen.org
    DOAB: www.doabooks.org

     

     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Differen formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    A logged-in user can export up to 15000 items. If you're not logged in, you can export no more than 500 items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.