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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Superior document: | Graduate Texts in Mathematics ; v.288 |
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Year of Publication: | 2021 |
Language: | English |
Series: | Graduate Texts in Mathematics
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Physical Description: | 1 online resource (877 p.) |
Notes: | Description based upon print version of record. |
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(CKB)5590000000518009 EBL6652280 (OCoLC)1258658936 (AU-PeEL)EBL6652280 (oapen)https://directory.doabooks.org/handle/20.500.12854/71303 (MiAaPQ)EBC6652280 (PPN)258059516 (EXLCZ)995590000000518009 |
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Voight, John (Mathematician) Quaternion Algebras. Cham : Springer International Publishing AG, 2021. 1 online resource (877 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier Graduate Texts in Mathematics ; v.288 1710008 Grado en Matemáticas Álgebra Lineal y Geometría II 2400011 Doble Grado en Física y Matemáticas Álgebra Lineal y Geometría II 2410010 Doble Grado en Matemáticas y Estadística Álgebra Lineal y Geometría II Description based upon print version of record. 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. English Dartmouth College Algebra bicssc Groups & group theory bicssc Number theory bicssc Quaternions thub Llibres electrònics thub 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 3-030-56692-7 Graduate Texts in Mathematics |
language |
English |
format |
eBook |
author |
Voight, John (Mathematician) |
spellingShingle |
Voight, John (Mathematician) Quaternion Algebras. Graduate Texts in Mathematics ; |
author_facet |
Voight, John (Mathematician) |
author_variant |
j v jv |
author_sort |
Voight, John (Mathematician) |
title |
Quaternion Algebras. |
title_full |
Quaternion Algebras. |
title_fullStr |
Quaternion Algebras. |
title_full_unstemmed |
Quaternion Algebras. |
title_auth |
Quaternion Algebras. |
title_new |
Quaternion Algebras. |
title_sort |
quaternion algebras. |
series |
Graduate Texts in Mathematics ; |
series2 |
Graduate Texts in Mathematics ; |
publisher |
Springer International Publishing AG, |
publishDate |
2021 |
physical |
1 online resource (877 p.) |
isbn |
3-030-56694-3 3-030-56692-7 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA251 |
callnumber-sort |
QA 3251.5 |
genre |
Llibres electrònics thub |
genre_facet |
Llibres electrònics |
illustrated |
Not Illustrated |
oclc_num |
1258658936 |
work_keys_str_mv |
AT voightjohn quaternionalgebras |
status_str |
n |
ids_txt_mv |
(CKB)5590000000518009 EBL6652280 (OCoLC)1258658936 (AU-PeEL)EBL6652280 (oapen)https://directory.doabooks.org/handle/20.500.12854/71303 (MiAaPQ)EBC6652280 (PPN)258059516 (EXLCZ)995590000000518009 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Graduate Texts in Mathematics ; v.288 |
is_hierarchy_title |
Quaternion Algebras. |
container_title |
Graduate Texts in Mathematics ; v.288 |
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