04562nam 22008293u 450 991048871890332120240522193056.03-030-56694-3(CKB)5590000000518009EBL6652280(OCoLC)1258658936(AU-PeEL)EBL6652280(oapen)https://directory.doabooks.org/handle/20.500.12854/71303(MiAaPQ)EBC6652280(PPN)258059516(EXLCZ)99559000000051800920220617d2021|||| u|| |engur|n|---|||||txtrdacontentcrdamediacrrdacarrierQuaternion AlgebrasCham Springer International Publishing AG20211 online resource (877 p.)Graduate Texts in Mathematics ;v.288Description based upon print version of record.3-030-56692-7 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.Graduate Texts in MathematicsAlgebrabicsscGroups & group theorybicsscNumber theorybicsscQuaternionsthubLlibres electrònicsthubAssociative Rings and AlgebrasGroup Theory and GeneralizationsNumber TheoryOpen AccessQuaternionsQuaternion algebrasQuaternion ordersQuaternion idealsNoncommutative algebraQuaternions and quadratic formsTernary quadratic formsSimple algebras and involutionsLattices and integral quadratic formsHurwitz orderQuaternion algebras over local fieldsQuaternion algebras over global fieldsAdelic frameworkIdelic zeta functionsQuaternions hyperbolic geometryQuaternions arithmetic groupsQuaternions arithmetic geometrySupersingular elliptic curvesAbelian surfaces with QMAlgebraGroups & group theoryAlgebraGroups & group theoryNumber theoryQuaternionsVoight John(Mathematician)1736755AU-PeELAU-PeELAU-PeELBOOK9910488718903321Quaternion Algebras4157087UNINA