Buildings: Theory and Applications
Buildings: Theory and Applications
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建筑：理论与应用
DOI：
10.1007/978-0-387-78835-7
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发表时间：
2008
影响因子：
0.5
通讯作者：
K. S. Brown
中科院分区：
文献类型：
--
作者：
P. Abramenko;K. S. Brown
* 包含前一本书《K的建筑》中的所有材料。S.布朗（一个简短的，友好的，基本的介绍理论的建筑物），并大幅修订，更新，新的材料
* 包括先进的内容，是适当的更先进的学生或自学，包括两个新的章节的Moufang财产
* 介绍了许多新的练习和插图，以及提示和解决方案-包括一个单独的，广泛的解决方案手册
* 彻底集中在所有三种方法的建筑物，“老式的”，组合（商会系统），和公制，使读者可以学习所有三个或只集中在一个
* 包括关于细胞复合体、根系和代数群的附录
这本书对待雅克山雀的美丽理论的建筑物，使理论接近读者与最小的背景。它包括了第二位作者的早期著作《建筑物》的所有材料，该书于1989年由斯普林格出版社出版，从古典（单纯）的角度介绍了建筑物。这本新书还包括两个其他方法的建筑物，这很好地补充了单纯的方法：一方面，建筑物可以被视为抽象的集室与外尔群值的距离函数;这一观点已成为越来越重要的理论和应用的建筑物。另一方面，建筑物可以被视为度量空间。初学者仍然可以使用新书的部分内容作为对建筑物的友好介绍，但这本书也包含了对积极研究者有价值的材料。
本书有几条路径，以便读者可以选择专注于一种特定的方法。在书的基本部分，步伐是温和的，风格是友好的整个。所有的概念都有很好的动机。有彻底的治疗先进的主题，如牟方财产，与论点，是更详细的比那些以前出现在文献中。
这本书适合作为教科书，有很多练习，也可以用来自学。
* Contains all of the material from the previous book, Buildings by K. S. Brown (a short, friendly, elementary introduction to the theory of buildings), and substantially revised, updated, new material
* Includes advanced content that is appropriate for more advanced students or for self-study, including two new chapters on the Moufang property
* Introduces many new exercises and illustrations, as well as hints and solutions—including a separate, extensive solutions manual
* Thoroughly focuses on all three approachs to buildings, “old-fashioned," combinatorial (chamber systems), and metric so that the reader can learn all three or focus on only one
* Includes appendices on cell complexes, root systems and algebraic groups
This book treats Jacques Tits's beautiful theory of buildings, making that theory accessible to readers with minimal background. It includes all the material of the earlier book Buildings by the second-named author, published by Springer-Verlag in 1989, which gave an introduction to buildings from the classical (simplicial) point of view. This new book also includes two other approaches to buildings, which nicely complement the simplicial approach: On the one hand, buildings may be viewed as abstract sets of chambers with a Weyl-group-valued distance function; this point of view has become increasingly important in the theory and applications of buildings. On the other hand, buildings may be viewed as metric spaces. Beginners can still use parts of the new book as a friendly introduction to buildings, but the book also contains valuable material for the active researcher.
There are several paths through the book, so that readers may choose to concentrate on one particular approach. The pace is gentle in the elementary parts of the book, and the style is friendly throughout. All concepts are well motivated. There are thorough treatments of advanced topics such as the Moufang property, with arguments that are much more detailed than those that have previously appeared in the literature.
This book is suitable as a textbook, with many exercises, and it may also be used for self-study.