LEADER 04583nam 22008293u 450 001 996466394403316 005 20240522193056.0 010 $a3-030-56694-3 035 $a(CKB)5590000000518009 035 $aEBL6652280 035 $a(OCoLC)1258658936 035 $a(AU-PeEL)EBL6652280 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/71303 035 $a(MiAaPQ)EBC6652280 035 $a(PPN)258059516 035 $a(EXLCZ)995590000000518009 100 $a20220617d2021|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aQuaternion Algebras$b[electronic resource] 210 $aCham $cSpringer International Publishing AG$d2021 215 $a1 online resource (877 p.) 225 1 $aGraduate Texts in Mathematics ;$vv.288 300 $aDescription based upon print version of record. 311 $a3-030-56692-7 330 $aThis 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. 410 0$aGraduate Texts in Mathematics 606 $aAlgebra$2bicssc 606 $aGroups & group theory$2bicssc 606 $aNumber theory$2bicssc 606 $aQuaternions$2thub 608 $aLlibres electrònics$2thub 610 $aAssociative Rings and Algebras 610 $aGroup Theory and Generalizations 610 $aNumber Theory 610 $aOpen Access 610 $aQuaternions 610 $aQuaternion algebras 610 $aQuaternion orders 610 $aQuaternion ideals 610 $aNoncommutative algebra 610 $aQuaternions and quadratic forms 610 $aTernary quadratic forms 610 $aSimple algebras and involutions 610 $aLattices and integral quadratic forms 610 $aHurwitz order 610 $aQuaternion algebras over local fields 610 $aQuaternion algebras over global fields 610 $aAdelic framework 610 $aIdelic zeta functions 610 $aQuaternions hyperbolic geometry 610 $aQuaternions arithmetic groups 610 $aQuaternions arithmetic geometry 610 $aSupersingular elliptic curves 610 $aAbelian surfaces with QM 610 $aAlgebra 610 $aGroups & group theory 615 7$aAlgebra 615 7$aGroups & group theory 615 7$aNumber theory 615 7$aQuaternions 700 $aVoight$b John$c(Mathematician)$01736755 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a996466394403316 996 $aQuaternion Algebras$94157087 997 $aUNISA