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作者 Boelaert, Lien, author
書名 Moufang sets and structurable division algebras / Lien Boelaert, Tom De Medts, Anastasia Stavrova
出版項 Providence, RI, USA : American Mathematical Society, [2019]
2019
國際標準書號 9781470435547
1470435543
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA247.45 B64 2019    尋找中    30340200563603
說明 v, 90 pages : illustrations ; 26 cm
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
系列 Memoirs of the American Mathematical Society, 0065-9266 ; number 1245
Memoirs of the American Mathematical Society ; no. 1245
附註 "May 2019, volume 259, number 1245 (second of 8 numbers)."
Includes bibliographical references (pages 87-90)
Introduction -- Chapter 1. Moufang sets -- Chapter 2. Structurable algebras -- Chapter 3. One-invertibility for structurable algebras -- Chapter 4. Simple structurable algebras and simple algebraic groups -- Chapter 5. Moufang sets and structurable division algebras -- Chapter 6. Examples -- Bibliography
"A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they are assumed to be conjugate and to generate the whole group. It has been known for some time that every Jordan division algebra gives rise to a Moufang set with abelian root groups. We extend this result by showing that every structurable division algebra gives rise to a Moufang set, and conversely, we show that every Moufang set arising from a simple linear algebraic group of relative rank one over an arbitrary field k of characteristic different from 2 and 3 arises from a structurable division algebra. We also obtain explicit formulas for the root groups, the T-map and the Hua maps of these Moufang sets. This is particularly useful for the Moufang sets arising from exceptional linear algebraic groups"-- Provided by publisher
主題 Division algebras
Moufang loops
Jordan algebras
Combinatorial group theory
Combinatorial group theory. fast (OCoLC)fst00868974
Division algebras. fast (OCoLC)fst00895800
Jordan algebras. fast (OCoLC)fst00983985
Moufang loops. fast (OCoLC)fst01028220
Associative rings and algebras {For the commutative case, see 13-XX} -- Rings and algebras with additional structure -- Rings with involution; Lie, Jordan and other nonassociative structures [See also. msc
Group theory and generalizations -- Structure and classification of infinite or finite groups -- Groups with a $BN$-pair; buildings [See also 51E24]. msc
Nonassociative rings and algebras -- General nonassociative rings -- Division algebras. msc
Nonassociative rings and algebras -- Lie algebras and Lie superalgebras {For Lie groups, see 22Exx} -- Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, msc
Nonassociative rings and algebras -- Lie algebras and Lie superalgebras {For Lie groups, see 22Exx} -- Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]. msc
Nonassociative rings and algebras -- Jordan algebras (algebras, triples and pairs). msc
Group theory and generalizations -- Linear algebraic groups and related topics {For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation the. msc
Alt Author Medts, Tom de, 1980- author
Stavrova, Anastasia, author
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