Quaternion Algebras
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 f...
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| Үндсэн зохиолч: | |
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| Формат: | Online |
| Хэл сонгох: | англи |
| Хэвлэсэн: |
Springer Nature
2021
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| Нөхцлүүд: | |
| Онлайн хандалт: | ONIX_20210714_9783030566944_8 |
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Шошго байхгүй, Энэхүү баримтыг шошголох эхний хүн болох!
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| _version_ | 1869531382972153856 |
|---|---|
| author | Voight, John |
| author_browse | Voight, John |
| author_facet | Voight, John |
| author_sort | Voight, John |
| collection | Directory of Open Access Books |
| description | 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. |
| format | Online |
| id | doab-20.500.12854ir-71303 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | Springer Nature |
| publisherStr | Springer Nature |
| record_format | ojs |
| spelling | doab-20.500.12854ir-713032025-08-13T14:12:29Z Quaternion Algebras Voight, John 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 Textbook thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PB Mathematics::PBG Groups and group theory thema EDItEUR::P Mathematics and Science::PB Mathematics::PBH Number theory thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PB Mathematics::PBG Groups and group theory thema EDItEUR::P Mathematics and Science::PB Mathematics::PBH Number theory 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. 2021-07-15T02:01:18Z 2021-07-15T02:01:18Z 2021-07-14T09:58:09Z 2021 book ONIX_20210714_9783030566944_8 OCN: 1258658936 https://library.oapen.org/handle/20.500.12657/50018 9783030566944 https://directory.doabooks.org/handle/20.500.12854/71303 eng Graduate Texts in Mathematics open access image/jpeg image/jpeg image/jpeg n/a n/a n/a https://library.oapen.org/bitstream/20.500.12657/50018/1/978-3-030-56694-4.pdf https://library.oapen.org/bitstream/20.500.12657/50018/1/978-3-030-56694-4.pdf https://library.oapen.org/bitstream/20.500.12657/50018/1/978-3-030-56694-4.pdf Springer Nature Springer International Publishing 10.1007/978-3-030-56694-4 10.1007/978-3-030-56694-4 9fa3421d-f917-4153-b9ab-fc337c396b5a Dartmouth College 4ef68025-6bcf-4f1d-9f1f-2ec8a51ede7d d313a31a-a2a5-45e9-9d16-71b81372884b 9783030566944 Springer International Publishing 885 [grantnumber unknown] [grantnumber unknown] open access |
| spellingShingle | 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 Textbook thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PB Mathematics::PBG Groups and group theory thema EDItEUR::P Mathematics and Science::PB Mathematics::PBH Number theory thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PB Mathematics::PBG Groups and group theory thema EDItEUR::P Mathematics and Science::PB Mathematics::PBH Number theory Voight, John Quaternion Algebras |
| title | Quaternion Algebras |
| title_full | Quaternion Algebras |
| title_fullStr | Quaternion Algebras |
| title_full_unstemmed | Quaternion Algebras |
| title_short | Quaternion Algebras |
| title_sort | quaternion algebras |
| topic | 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 Textbook thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PB Mathematics::PBG Groups and group theory thema EDItEUR::P Mathematics and Science::PB Mathematics::PBH Number theory thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PB Mathematics::PBG Groups and group theory thema EDItEUR::P Mathematics and Science::PB Mathematics::PBH Number theory |
| topic_facet | 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 Textbook thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PB Mathematics::PBG Groups and group theory thema EDItEUR::P Mathematics and Science::PB Mathematics::PBH Number theory thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PB Mathematics::PBG Groups and group theory thema EDItEUR::P Mathematics and Science::PB Mathematics::PBH Number theory |
| url | ONIX_20210714_9783030566944_8 |
| work_keys_str_mv | AT voightjohn quaternionalgebras |