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010 a| 2022007637;

020 a| 9781470451011q| (paperback);

020 z| 9781470470180q| (epub);

035 a| (WaSeSS)ssj0002594793;

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084 a| 17C40a| 20E42a| 51E12a| 51E242| msc;

100 1 a| Mühlherr, Bernhard Matthias.=| ^A1333991;

245 10 a| Tits polygonsh| [electronic resource] /c| Bernhard Mühlherr, Richard M. Weiss ; with an appendix by Holger P. Petersson.;

260 a| Providence, RI :b| American Mathematical Society,c| [2022];

300 a| xi, 114 pages ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| number 1352;

500 a| "January 2022, volume 275, number 1352 (sixth of 6 numbers).";

504 a| Includes bibliographical references and index.;

505 0 a| Tits polygons -- Tits hexagons -- Groups of relative rank 1 -- Appendix / by Holger P. Petersson.;

506 a| Available only to authorized users.;

520 a| "We introduce the notion of a Tits polygon, a generalization of the notion of a Moufang polygon, and show that Tits polygons arise in a natural way from certain configurations of parabolic subgroups in an arbitrary spherical buildings satisfying the Moufang condition. We establish numerous basic properties of Tits polygons and characterize a large class of Tits hexagons in terms of Jordan algebras. We apply this classification to give a "rank 2" presentation for the group of F-rational points of an arbitrary exceptional simple group of F-rank at least 4 and to determine defining relations for the group of F-rational points of an an arbitrary group of Frank 1 and absolute type D4, E6, E7 or E8 associated to the unique vertex of the Dynkin diagram that is not orthogonal to the highest root. All of these results are over a field of arbitrary characteristic"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Moufang loops.=| ^A99021;

650 0 a| Jordan algebras.=| ^A45522;

650 0 a| Buildings (Group theory)=| ^A249487;

650 0 a| Graph theory.=| ^A31040;

650 0 a| Polygons.=| ^A72581;

650 7 a| Nonassociative rings and algebras -- Jordan algebras (algebras, triples and pairs) -- Exceptional Jordan structures.2| msc;

650 7 a| Group theory and generalizations -- Structure and classification of infinite or finite groups -- Groups with a $BN$-pair; buildings.2| msc;

650 7 a| Geometry -- Finite geometry and special incidence structures -- Generalized quadrangles, generalized polygons.2| msc;

650 7 a| Geometry -- Finite geometry and special incidence structures -- Buildings and the geometry of diagrams.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Weiss, Richard M.q| (Richard Mark),d| 1946-=| ^A531383;

700 1 a| Petersson, Holger P.,d| 1939-=| ^A1328931;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6852909;

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999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6516794-2001l| HSLELECm| HSLr| Ys| Yt| HEBKu| 1/14/2025x| EBOOKz| HERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6516794-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 1/14/2025x| EBOOKz| JERESOURCE;

Tits polygons / Bernhard Mühlherr, Richard M. Weiss ; with an appendix by Holger P. Petersson.

Author/creator	Mühlherr, Bernhard Matthias
Other author	Weiss, Richard M. (Richard Mark), 1946-
Other author	Petersson, Holger P., 1939-
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, [2022]
Description	xi, 114 pages ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Moufang loops. Jordan algebras. Buildings (Group theory) Graph theory. Polygons.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; number 1352
Contents	Tits polygons -- Tits hexagons -- Groups of relative rank 1 -- Appendix / by Holger P. Petersson.
Abstract	"We introduce the notion of a Tits polygon, a generalization of the notion of a Moufang polygon, and show that Tits polygons arise in a natural way from certain configurations of parabolic subgroups in an arbitrary spherical buildings satisfying the Moufang condition. We establish numerous basic properties of Tits polygons and characterize a large class of Tits hexagons in terms of Jordan algebras. We apply this classification to give a "rank 2" presentation for the group of F-rational points of an arbitrary exceptional simple group of F-rank at least 4 and to determine defining relations for the group of F-rational points of an an arbitrary group of Frank 1 and absolute type D4, E6, E7 or E8 associated to the unique vertex of the Dynkin diagram that is not orthogonal to the highest root. All of these results are over a field of arbitrary characteristic"-- Provided by publisher.
General note	"January 2022, volume 275, number 1352 (sixth of 6 numbers)."
Bibliography note	Includes bibliographical references and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022007637
ISBN	9781470451011 (paperback)
ISBN	(epub)

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