國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Quaternion algebras

SpringerLink (Online service)

Quaternion algebras

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Quaternion algebrasby John Voight.
作者:	Voight, John.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	xxiii, 885 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Quaternions.
電子資源:	https://doi.org/10.1007/978-3-030-56694-4
ISBN:	9783030566944$q(electronic bk.)

Quaternion algebras
Voight, John.

Quaternion algebras[electronic resource] /by John Voight. - Cham :Springer International Publishing :2021. - xxiii, 885 p. :ill., digital ;24 cm. - Graduate texts in mathematics,2880072-5285 ;. - Graduate texts in mathematics ;129..

1. Introduction -- 2. Beginnings -- 3. Involutions -- 4. Quadratic Forms -- 5. Ternary Quadratic Forms -- 6. Characteristic 2 -- 7. Simple Algebras -- 8. Simple Algebras and Involutions -- 9. Lattices and Integral Quadratic Forms -- 10. Orders -- 11. The Hurwitz Order -- 12. Ternary Quadratic Forms Over Local Fields -- 13. Quaternion Algebras Over Local Fields -- 14. Quaternion Algebras Over Global Fields -- 15. Discriminants -- 16. Quaternion Ideals and Invertability -- 17. Classes of Quaternion Ideals -- 18. Picard Group -- 19. Brandt Groupoids -- 20. Integral Representation Theory -- 21. Hereditary and Extremal Orders -- 22. Ternary Quadratic Forms -- 23. Quaternion Orders -- 24. Quaternion Orders: Second Meeting -- 25. The Eichler Mass Formula -- 26. Classical Zeta Functions -- 27. Adelic Framework -- 28. Strong Approximation -- 29. Idelic Zeta Functions -- 30. Optimal Embeddings -- 31. Selectivity -- 32. Unit Groups -- 33. Hyperbolic Plane -- 34. Discrete Group Actions -- 35. Classical Modular Group -- 36. Hyperbolic Space -- 37. Fundamental Domains -- 38. Quaternionic Arithmetic Groups -- 39. Volume Formula -- 40. Classical Modular Forms -- 41. Brandt Matrices -- 42. Supersingular Elliptic Curves -- 43. Abelian Surfaces with QM.

Open access.

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.

ISBN: 9783030566944$q(electronic bk.)

Standard No.: 10.1007/978-3-030-56694-4doiSubjects--Topical Terms:

466750
Quaternions.

LC Class. No.: QA196

Dewey Class. No.: 512.5

Quaternion algebras
LDR:04278nmm a2200349 a 4500 001 602520
003 DE-He213
005 20210703131259.0
006 m d
007 cr nn 008maaau
008 211112s2021 sz s 0 eng d
020 $a 9783030566944$q(electronic bk.)
020 $a 9783030566920$q(paper)
024 7 $a 10.1007/978-3-030-56694-4 $2 doi
035 $a 978-3-030-56694-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA196
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.5 $2 23
090 $a QA196 $b .V889 2021
100 1 $a Voight, John. $3 898233
245 1 0 $a Quaternion algebras $h [electronic resource] / $c by John Voight.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xxiii, 885 p. : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 0072-5285 ; $v 288
505 0 $a 1. Introduction -- 2. Beginnings -- 3. Involutions -- 4. Quadratic Forms -- 5. Ternary Quadratic Forms -- 6. Characteristic 2 -- 7. Simple Algebras -- 8. Simple Algebras and Involutions -- 9. Lattices and Integral Quadratic Forms -- 10. Orders -- 11. The Hurwitz Order -- 12. Ternary Quadratic Forms Over Local Fields -- 13. Quaternion Algebras Over Local Fields -- 14. Quaternion Algebras Over Global Fields -- 15. Discriminants -- 16. Quaternion Ideals and Invertability -- 17. Classes of Quaternion Ideals -- 18. Picard Group -- 19. Brandt Groupoids -- 20. Integral Representation Theory -- 21. Hereditary and Extremal Orders -- 22. Ternary Quadratic Forms -- 23. Quaternion Orders -- 24. Quaternion Orders: Second Meeting -- 25. The Eichler Mass Formula -- 26. Classical Zeta Functions -- 27. Adelic Framework -- 28. Strong Approximation -- 29. Idelic Zeta Functions -- 30. Optimal Embeddings -- 31. Selectivity -- 32. Unit Groups -- 33. Hyperbolic Plane -- 34. Discrete Group Actions -- 35. Classical Modular Group -- 36. Hyperbolic Space -- 37. Fundamental Domains -- 38. Quaternionic Arithmetic Groups -- 39. Volume Formula -- 40. Classical Modular Forms -- 41. Brandt Matrices -- 42. Supersingular Elliptic Curves -- 43. Abelian Surfaces with QM.
506 $a Open access.
520 $a 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.
650 0 $a Quaternions. $3 466750
650 0 $a Functions, Quaternion. $3 678655
650 1 4 $a Associative Rings and Algebras. $3 274818
650 2 4 $a Group Theory and Generalizations. $3 274819
650 2 4 $a Number Theory. $3 274059
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Graduate texts in mathematics ; $v 129. $3 436082
856 4 0 $u https://doi.org/10.1007/978-3-030-56694-4
950 $a Mathematics and Statistics (SpringerNature-11649)