Croching
发表于 2025-3-21 17:30:22
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传授知识
发表于 2025-3-21 22:44:51
by teaching a graduate course on it at Cornell University in Spring 1987. This book is based on the not es from that course. The course started from scratch and proceeded at a leisurely pace. The book therefore does not get very far. Indeed, the definition of the term "building" doesn‘t even appear
RECUR
发表于 2025-3-22 04:17:33
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VICT
发表于 2025-3-22 05:10:20
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Criteria
发表于 2025-3-22 11:49:17
Finite Reflection Groups,flections. In order to avoid technicalities in this introductory chapter, we confine our attention to . groups and we require our reflections to be with respect to . hyperplanes (i.e., hyperplanes passing through the origin). We will generalize this in Chapter VI, replacing “finite” by “discrete” an
nephritis
发表于 2025-3-22 16:02:41
Abstract Reflection Groups,by a subset . consisting of elements of order 2. Define, as in Chapter I, a . to be a coset .(.′) with ω ∈ . and .′ ⊆ .. Now . ∑ = ∑(., .) to be the poset of special cosets, ordered by the opposite of the inclusion relation: . ≤. in ∑ if and only if . ⊇. as subsets of ., in which case we say that .
不能和解
发表于 2025-3-22 19:20:34
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使满足
发表于 2025-3-22 23:44:45
Buildings, to motivate this definition. In particular, you will probably wonder how someone (namely, Tits) came up with these axioms. I will not attempt to answer this question now, but I will make some historical remarks in the next chapter (§V.4) which should make the definition seem less mysterious.
同时发生
发表于 2025-3-23 04:51:18
Buildings and Groups,goes along with the theory of Coxeter complexes. In particular, we will discover a class of groups . for which we can construct an associated building Δ, on which . acts as a group of type-preserving simplicial automorphisms.
疾驰
发表于 2025-3-23 06:59:42
Applications to Group Cohomology,chapter is a familiarity with the basic facts about group cohomology, as given for instance in . I will also use some algebraic topology (fundamental group, covering spaces, homology theory of manifolds, etc.).