樓理論及其在幾何和拓?fù)渲械膽?yīng)用（英）

　　本書(shū)的內(nèi)容是關(guān)于樓（building）理論及其在幾何和拓?fù)渲械膽?yīng)用。樓作為一種組合和幾何結(jié)構(gòu)由Jacques Tits引入，作為理解任意域上保距還原線性代數(shù)群結(jié)構(gòu)的一種方法，Tits因此項(xiàng)工作獲得2008年Abel獎(jiǎng)。樓理論是研究代數(shù)群及其表示的必要工具，在幾個(gè)相當(dāng)不同的領(lǐng)域中具有重要應(yīng)用。本書(shū)的第一部分是作者專(zhuān)為國(guó)內(nèi)學(xué)生學(xué)習(xí)樓理論準(zhǔn)備的導(dǎo)讀資料，其中特別注重利用例子說(shuō)明問(wèn)題，可讀性很強(qiáng)；第二部分則綜述了樓理論在幾何與拓?fù)浞矫娴膽?yīng)用，不僅總結(jié)了近些年樓理論研究的成就，還提出了未來(lái)的研究方向。本書(shū)是一本觀點(diǎn)較高、極具學(xué)術(shù)價(jià)值的數(shù)學(xué)學(xué)習(xí)資料，可供我國(guó)高等院校代數(shù)及相關(guān)專(zhuān)業(yè)作為教學(xué)參考書(shū)使用。 Symmetry is an essential concept in mathematics， science and daily life， and an effective mathematical tool to describe symmetry is the notion of groups. For example， the symmetries of the regular solids （or Platonic solids） are described by the finite subgroups of the rotation group SO（3）. Therefore， finding the symmetry group of a geometric object or space is a classical and important problem. On the other hand， given a group， how to find a natural geometric space which realizes the group as its symmetries is also interesting and fruitful. One of the most useful or beautiful class of groups consists of algebraic groups， and their corresponding geometric spaces are given by Tits buildings. Originally introduced by Tits to give a geometric description of exceptional simple algebraic groups， buildings have turned out to be extremely useful in a broad range of subjects in contemporary mathematics， including algebra， geometry， topology， number theory， and analysis etc. Since the theory of algebraic groups is complicated， the theory of buildings can be technical and demanding by itself. This book gives an accessible approach by using elementary and concrete examples and by emphasizing many applications in many seemingly unrelated subjects. The reader will learn from this book what buildings are， why they are useful， and how they can be used.

暫缺《樓理論及其在幾何和拓?fù)渲械膽?yīng)用（英）》作者簡(jiǎn)介