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Quaternion Algebras [[electronic resource]]



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Autore: Voight John (Mathematician) Visualizza persona
Titolo: Quaternion Algebras [[electronic resource]] Visualizza cluster
Pubblicazione: Cham, : Springer International Publishing AG, 2021
Descrizione fisica: 1 online resource (877 p.)
Soggetto topico: Algebra
Groups & group theory
Number theory
Quaternions
Soggetto genere / forma: Llibres electrònics
Soggetto non controllato: 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
Note generali: Description based upon print version of record.
Sommario/riassunto: 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.
Titolo autorizzato: Quaternion Algebras  Visualizza cluster
ISBN: 3-030-56694-3
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 996466394403316
Lo trovi qui: Univ. di Salerno
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Serie: Graduate Texts in Mathematics