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dc.contributor.authorVoight, John
dc.date.accessioned2021-07-14T09:58:09Z
dc.date.available2021-07-14T09:58:09Z
dc.date.issued2021
dc.identifierONIX_20210714_9783030566944_8
dc.identifier.urihttps://library.oapen.org/handle/20.500.12657/50018
dc.description.abstractThis 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.
dc.languageEnglish
dc.relation.ispartofseriesGraduate Texts in Mathematics
dc.subject.classificationthema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebraen_US
dc.subject.classificationthema EDItEUR::P Mathematics and Science::PB Mathematics::PBG Groups and group theoryen_US
dc.subject.classificationthema EDItEUR::P Mathematics and Science::PB Mathematics::PBH Number theoryen_US
dc.subject.otherAssociative Rings and Algebras
dc.subject.otherGroup Theory and Generalizations
dc.subject.otherNumber Theory
dc.subject.otherOpen Access
dc.subject.otherQuaternions
dc.subject.otherQuaternion algebras
dc.subject.otherQuaternion orders
dc.subject.otherQuaternion ideals
dc.subject.otherNoncommutative algebra
dc.subject.otherQuaternions and quadratic forms
dc.subject.otherTernary quadratic forms
dc.subject.otherSimple algebras and involutions
dc.subject.otherLattices and integral quadratic forms
dc.subject.otherHurwitz order
dc.subject.otherQuaternion algebras over local fields
dc.subject.otherQuaternion algebras over global fields
dc.subject.otherAdelic framework
dc.subject.otherIdelic zeta functions
dc.subject.otherQuaternions hyperbolic geometry
dc.subject.otherQuaternions arithmetic groups
dc.subject.otherQuaternions arithmetic geometry
dc.subject.otherSupersingular elliptic curves
dc.subject.otherAbelian surfaces with QM
dc.subject.otherAlgebra
dc.subject.otherGroups & group theory
dc.titleQuaternion Algebras
dc.typebook
oapen.identifier.doi10.1007/978-3-030-56694-4
oapen.relation.isPublishedBy6c6992af-b843-4f46-859c-f6e9998e40d5
oapen.relation.isFundedBy4ef68025-6bcf-4f1d-9f1f-2ec8a51ede7d
oapen.relation.isFundedByd313a31a-a2a5-45e9-9d16-71b81372884b
oapen.relation.isbn9783030566944
oapen.imprintSpringer International Publishing
oapen.series.number288
oapen.pages885
oapen.grant.number[grantnumber unknown]
oapen.grant.number[grantnumber unknown]


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