Tits polygons

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 prop...

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Hauptverfasser: Mühlherr, Bernhard, Weiss, Richard, Petersson, Holger P.
Format: E-Book Buch
Sprache:Englisch
Veröffentlicht: Providence, Rhode Island American Mathematical Society 2022
Ausgabe:1
Schriftenreihe:Memoirs of the American Mathematical Society
Schlagworte:
Buildings (Group theory)
Geometry > Finite geometry and special incidence structures > Buildings and the geometry of diagrams. msc
Geometry > Finite geometry and special incidence structures > Generalized quadrangles, generalized polygons. msc
Graph theory
Group theory and generalizations > Structure and classification of infinite or finite groups > Groups with a $BN$-pair; buildings. msc
Jordan algebras
Moufang loops
Nonassociative rings and algebras > Jordan algebras (algebras, triples and pairs) > Exceptional Jordan structures. msc
Polygons
descent
Moufang sets
Moufang polygons
buildings
ISBN:1470451018, 9781470451011
ISSN:0065-9266, 1947-6221
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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
AbstractList View the 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
Author Weiss, Richard
Petersson, Holger P.
Mühlherr, Bernhard
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  fullname: Weiss, Richard
– sequence: 3
  givenname: Holger P.
  surname: Petersson
  fullname: Petersson, Holger P.
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Keywords descent
Moufang sets
Moufang polygons
buildings
LCCN 2022007637
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Notes January 2022, volume 275, number 1352 (sixth of 6 numbers)
Includes bibliographical references (p. 111-112)
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Snippet 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...
View the abstract.
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SubjectTerms Buildings (Group theory)
Geometry -- Finite geometry and special incidence structures -- Buildings and the geometry of diagrams. msc
Geometry -- Finite geometry and special incidence structures -- Generalized quadrangles, generalized polygons. msc
Graph theory
Group theory and generalizations -- Structure and classification of infinite or finite groups -- Groups with a $BN$-pair; buildings. msc
Jordan algebras
Moufang loops
Nonassociative rings and algebras -- Jordan algebras (algebras, triples and pairs) -- Exceptional Jordan structures. msc
Polygons
TableOfContents Introduction -- Tits polygons -- Tits hexagons -- Groups of relative rank 1 -- Appendix by Holger P. Petersson
Cover -- Title page -- Introduction -- Acknowledgment -- Chapter 1. Tits polygons -- 1.1. Basic definitions -- 1.2. Examples -- 1.3. Commutator relations -- 1.4. Opposite roots -- 1.5. Uniqueness -- 1.6. A bound on -- Chapter 2. Tits hexagons -- 2.1. Cubic norm structures -- 2.2. Hexagons -- 2.3. Coordinates for Δ -- 2.4. Hexagons of polar type -- 2.5. The associated cubic norm structure -- 2.6. Automorphisms and classification -- Chapter 3. Groups of relative rank 1 -- 3.1. Descent -- 3.2. The subgraph Λ -- 3.3. The Galois involution -- 3.4. The Moufang set (Δ,⟨ ⟩) -- 3.5. The structure map -- 3.6. The generic case -- 3.7. A formula for -- 3.8. Arbitrary Galois groups -- Chapter 4. Appendix by Holger P. Petersson -- 4.1. Cubic norm structures -- 4.2. The cubic norm structure ℋ( , ) -- 4.3. Irreducibility of the structure group -- Bibliography -- Index -- Back Cover
Title Tits polygons
URI https://www.ams.org/memo/1352/
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Volume 275
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