The Structure Of Spherical Buildings
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| Author | : Richard M. Weiss |
| Publisher | : Princeton University Press |
| Total Pages | : 154 |
| Release | : 2020-07-21 |
| Genre | : Business & Economics |
| ISBN | : 0691216045 |
This book provides a clear and authoritative introduction to the theory of buildings, a topic of central importance to mathematicians interested in the geometric aspects of group theory. Its detailed presentation makes it suitable for graduate students as well as specialists. Richard Weiss begins with an introduction to Coxeter groups and goes on to present basic properties of arbitrary buildings before specializing to the spherical case. Buildings are described throughout in the language of graph theory. The Structure of Spherical Buildings includes a reworking of the proof of Jacques Tits's Theorem 4.1.2. upon which Tits's classification of thick irreducible spherical buildings of rank at least three is based. In fact, this is the first book to include a proof of this famous result since its original publication. Theorem 4.1.2 is followed by a systematic study of the structure of spherical buildings and their automorphism groups based on the Moufang property. Moufang buildings of rank two were recently classified by Tits and Weiss. The last chapter provides an overview of the classification of spherical buildings, one that reflects these and other important developments.
| Author | : Richard M. Weiss |
| Publisher | : Princeton University Press |
| Total Pages | : 154 |
| Release | : 2003 |
| Genre | : Architecture |
| ISBN | : 9780691117331 |
This book provides a clear and authoritative introduction to the theory of buildings, a topic of central importance to mathematicians interested in the geometric aspects of group theory. Its detailed presentation makes it suitable for graduate students as well as specialists. Richard Weiss begins with an introduction to Coxeter groups and goes on to present basic properties of arbitrary buildings before specializing to the spherical case. Buildings are described throughout in the language of graph theory. The Structure of Spherical Buildings includes a reworking of the proof of Jacques Tits's Theorem 4.1.2. upon which Tits's classification of thick irreducible spherical buildings of rank at least three is based. In fact, this is the first book to include a proof of this famous result since its original publication. Theorem 4.1.2 is followed by a systematic study of the structure of spherical buildings and their automorphism groups based on the Moufang property. Moufang buildings of rank two were recently classified by Tits and Weiss. The last chapter provides an overview of the classification of spherical buildings, one that reflects these and other important developments.
| Author | : Richard Mark Weiss |
| Publisher | : Princeton University Press |
| Total Pages | : 388 |
| Release | : 2009 |
| Genre | : Architecture |
| ISBN | : 9780691138817 |
Richard Weiss gives a detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. The book includes numerous results about automorphisms, completions and residues of these buildings.
| Author | : Katrin Tent |
| Publisher | : Cambridge University Press |
| Total Pages | : 314 |
| Release | : 2002-01-03 |
| Genre | : Mathematics |
| ISBN | : 9780521010634 |
Introduction to buildings and their geometries with emphasis on model theoretic constructions, covering recent developments.
| Author | : Stefan Witzel |
| Publisher | : Springer |
| Total Pages | : 128 |
| Release | : 2014-07-16 |
| Genre | : Mathematics |
| ISBN | : 3319064770 |
Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places. While the proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory of twin buildings.
| Author | : Jian Zhang |
| Publisher | : CRC Press |
| Total Pages | : 611 |
| Release | : 2020-11-04 |
| Genre | : Technology & Engineering |
| ISBN | : 100017865X |
Experimental Vibration Analysis for Civil Structures: Testing, Sensing, Monitoring, and Control covers a wide range of topics in the areas of vibration testing, instrumentation, and analysis of civil engineering and critical infrastructure. It explains how recent research, development, and applications in experimental vibration analysis of civil engineering structures have progressed significantly due to advancements in the fields of sensor and testing technologies, instrumentation, data acquisition systems, computer technology, computational modeling and simulation of large and complex civil infrastructure systems. The book also examines how cutting-edge artificial intelligence and data analytics can be applied to infrastructure systems. Features: Explains how recent technological developments have resulted in addressing the challenge of designing more resilient infrastructure Examines numerous research studies conducted by leading scholars in the field of infrastructure systems and civil engineering Presents the most emergent fields of civil engineering design, such as data analytics and Artificial Intelligence for the analysis and performance assessment of infrastructure systems and their resilience Emphasizes the importance of an interdisciplinary approach to develop the modeling, analysis, and experimental tools for designing more resilient and intelligent infrastructures Appropriate for practicing engineers and upper-level students, Experimental Vibration Analysis for Civil Structures: Testing, Sensing, Monitoring, and Control serves as a strategic roadmap for further research in the field of vibration testing and instrumentation of infrastructure systems.
| Author | : Li Tian |
| Publisher | : Trans Tech Publications Ltd |
| Total Pages | : 1770 |
| Release | : 2013-08-08 |
| Genre | : Technology & Engineering |
| ISBN | : 3038261556 |
Selected, peer reviewed papers from the 2013 International Conference on Civil, Architecture and Building Materials (3rd CEABM 2013), May 24-26, 2013, Jinan, China
| Author | : Rune Jakobsen |
| Publisher | : BoD – Books on Demand |
| Total Pages | : 290 |
| Release | : 2012 |
| Genre | : Architecture |
| ISBN | : 8771149317 |
This is a book about architecture and astronomy and it combines disciplines from both fields. Astronomic objects can provide inspiration for architecture, and the science of construction and perspective in architecture can describe the processes that take place in the Universe.
| Author | : Katrin Tent |
| Publisher | : Cambridge University Press |
| Total Pages | : 327 |
| Release | : 2008-10-16 |
| Genre | : Mathematics |
| ISBN | : 0521717884 |
Many areas of mathematics were deeply influenced or even founded by Hermann Weyl, including geometric foundations of manifolds and physics, topological groups, Lie groups and representation theory, harmonic analysis and analytic number theory as well as foundations of mathematics. In this volume, leading experts present his lasting influence on current mathematics, often connecting Weyl's theorems with cutting edge research in dynamical systems, invariant theory, and partial differential equations. In a broad and accessible presentation, survey chapters describe the historical development of each area alongside up-to-the-minute results, focussing on the mathematical roots evident within Weyl's work.
| Author | : Christian Bär |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 520 |
| Release | : 2011-12-18 |
| Genre | : Mathematics |
| ISBN | : 3642228429 |
This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.
