{"product_id":"albert-algebras-over-commutative-rings-the-last-frontier-of-jordan-systems-hardback-9781009426855","title":"Albert Algebras over Commutative Rings; The Last Frontier of Jordan Systems (Hardback) 9781009426855","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAlbert Algebras over Commutative Rings\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eThe Last Frontier of Jordan Systems\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eThe first comprehensive book on Albert algebras, the Jordan algebras that are most important for Lie algebras and exceptional groups.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eSkip Garibaldi (Author), Holger P. Petersson (Author), Michel L. Racine (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009426855, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 21 November 2024\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e678 pages\u003cbr\u003e23.5 x 15.9 x 4.1 cm, 1.09 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eAlbert algebras provide key tools for understanding exceptional groups and related structures such as symmetric spaces. This self-contained book provides the first comprehensive reference on Albert algebras over fields without any restrictions on the characteristic of the field. As well as covering results in characteristic 2 and 3, many results are proven for Albert algebras over an arbitrary commutative ring, showing that they hold in this greater generality. The book extensively covers requisite knowledge, such as non-associative algebras over commutative rings, scalar extensions, projective modules, alternative algebras, and composition algebras over commutative rings, with a special focus on octonion algebras. It then goes into Jordan algebras, Lie algebras, and group schemes, providing exercises so readers can apply concepts. This centralized resource illuminates the interplay between results that use only the structure of Albert algebras and those that employ theorems about group schemes, and is ideal for mathematics and physics researchers.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eI. Prologue: the ancient protagonists\u003cbr\u003e II. Foundations\u003cbr\u003e III. Alternative algebras\u003cbr\u003e IV. Composition algebras\u003cbr\u003e V. Jordan algebras\u003cbr\u003e VI. Cubic Jordan algebras\u003cbr\u003e VII. The two Tits constructions\u003cbr\u003e VIII. Lie algebras\u003cbr\u003e IX. Group schemes\u003cbr\u003e References\u003cbr\u003e Index of notation\u003cbr\u003e Subject index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Algebra [\u003ca title=\"See our other books on Algebra\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Algebra%20%5BPBF%5D%22\"\u003ePBF\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52474982433048,"sku":"9781009426855","price":114.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009426855i.jpg?v=1785802464","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/albert-algebras-over-commutative-rings-the-last-frontier-of-jordan-systems-hardback-9781009426855","provider":"Freshly Printed Books","version":"1.0","type":"link"}