Moufang Polygons
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Moufang Polygons
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Author : Jacques Tits
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Moufang Polygons written by Jacques Tits and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book gives the complete classification of Moufang polygons, starting from first principles. In particular, it may serve as an introduction to the various important algebraic concepts which arise in this classification including alternative division rings, quadratic Jordan division algebras of degree three, pseudo-quadratic forms, BN-pairs and norm splittings of quadratic forms. This book also contains a new proof of the classification of irreducible spherical buildings of rank at least three based on the observation that all the irreducible rank two residues of such a building are Moufang polygons. In an appendix, the connection between spherical buildings and algebraic groups is recalled.
Moufang Polygons
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Author : Jacques Tits
language : en
Publisher:
Release Date : 2014-01-15
Moufang Polygons written by Jacques Tits and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Moufang Polygons
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Author : Jacques Tits
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-09-12
Moufang Polygons written by Jacques Tits and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-12 with Mathematics categories.
This book gives the complete classification of Moufang polygons, starting from first principles. In particular, it may serve as an introduction to the various important algebraic concepts which arise in this classification including alternative division rings, quadratic Jordan division algebras of degree three, pseudo-quadratic forms, BN-pairs and norm splittings of quadratic forms. This book also contains a new proof of the classification of irreducible spherical buildings of rank at least three based on the observation that all the irreducible rank two residues of such a building are Moufang polygons. In an appendix, the connection between spherical buildings and algebraic groups is recalled.
Generalized Polygons
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Author : Hendrik,van Maldeghem
language : en
Publisher: Birkhäuser
Release Date : 2013-11-09
Generalized Polygons written by Hendrik,van Maldeghem and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with Mathematics categories.
This book is intended to be an introduction to the fascinating theory ofgeneralized polygons for both the graduate student and the specialized researcher in the field. It gathers together a lot of basic properties (some of which are usually referred to in research papers as belonging to folklore) and very recent and sometimes deep results. I have chosen a fairly strict geometrical approach, which requires some knowledge of basic projective geometry. Yet, it enables one to prove some typically group-theoretical results such as the determination of the automorphism groups of certain Moufang polygons. As such, some basic group-theoretical knowledge is required of the reader. The notion of a generalized polygon is a relatively recent one. But it is one of the most important concepts in incidence geometry. Generalized polygons are the building bricks of Tits buildings. They are the prototypes and precursors of more general geometries such as partial geometries, partial quadrangles, semi-partial ge ometries, near polygons, Moore geometries, etc. The main examples of generalized polygons are the natural geometries associated with groups of Lie type of relative rank 2. This is where group theory comes in and we come to the historical raison d'etre of generalized polygons. In 1959 Jacques Tits discovered the simple groups of type 3D by classifying the 4 trialities with at least one absolute point of a D -geometry. The method was 4 predominantly geometric, and so not surprisingly the corresponding geometries (the twisted triality hexagons) came into play. Generalized hexagons were born.
Spherical Building And Moufang Polygons
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Author : Andrea Villa
language : it
Publisher:
Release Date : 2009
Spherical Building And Moufang Polygons written by Andrea Villa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Connectedness Of Opposite Flag Geometries In Moufang Polygons
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Author : Peter Abramenko
language : en
Publisher:
Release Date : 1998
Connectedness Of Opposite Flag Geometries In Moufang Polygons written by Peter Abramenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
An Algebraic Structure For Moufang Quadrangles
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Author : Tom de Medts
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
An Algebraic Structure For Moufang Quadrangles written by Tom de Medts and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Features an article that intends to present a uniform algebraic structure for Moufang quadrangles, and to classify these structures without referring back to the original Moufang quadrangles from which they arise, thereby also giving a new proof for the classification of Moufang quadrangles, which does consist of the division into these 2 parts.
Generalized Polygons
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Author : Hendrik Van Maldeghem
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-05
Generalized Polygons written by Hendrik Van Maldeghem and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-05 with Mathematics categories.
Generalized Polygons is the first book to cover, in a coherent manner, the theory of polygons from scratch. In particular, it fills elementary gaps in the literature and gives an up-to-date account of current research in this area, including most proofs, which are often unified and streamlined in comparison to the versions generally known. Generalized Polygons will be welcomed both by the student seeking an introduction to the subject as well as the researcher who will value the work as a reference. In particular, it will be of great value for specialists working in the field of generalized polygons (which are, incidentally, the rank 2 Tits-buildings) or in fields directly related to Tits-buildings, incidence geometry and finite geometry. The approach taken in the book is of geometric nature, but algebraic results are included and proven (in a geometric way!). A noteworthy feature is that the book unifies and generalizes notions, definitions and results that exist for quadrangles, hexagons, octagons - in the literature very often considered separately - to polygons. Many alternative viewpoints given in the book heighten the sense of beauty of the subject and help to provide further insight into the matter.
Tits Polygons
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Author : Bernhard Mühlherr
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-02
Tits Polygons written by Bernhard Mühlherr and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-02 with Mathematics categories.
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Tits Buildings And The Model Theory Of Groups
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Author : Katrin Tent
language : en
Publisher: Cambridge University Press
Release Date : 2002-01-03
Tits Buildings And The Model Theory Of Groups written by Katrin Tent and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-03 with Mathematics categories.
Introduction to buildings and their geometries with emphasis on model theoretic constructions, covering recent developments.