Talk:Building (mathematics)
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Formal definition
editI don't find a formal definition of a building in the article, only applications and examples... --130.83.244.131 19:43, 22 June 2007 (UTC)
- It's a valid point. I plan on expanding the formal part eventually, but it gets very technical very fast. Not the least of the problems is a choice between two possible axiomatics of buildings, one based on simplicial complexes (Tits 1974, Brown 1989) and the other based on the notion of a chamber system (1981 paper of Tits, Ronan 1989). Arcfrk 19:57, 22 June 2007 (UTC)
- Related: the picture is very nice but it is not connected to anything in the text.
- It must be explained somewhere how is this the Bruhat-Tits building, no? Mamuka Jibladze (talk) 09:18, 13 June 2022 (UTC)
Tits building redirects here
edit- "Tits building" redirects here. For a building in which breasts are shown, see Strip club.
I'm not feeling bold enough to put that into the article. --Damian Yerrick (serious | business) 01:40, 16 November 2007 (UTC)
tesselations with regular (n-1)-simplices
editA tesselation of the n-dimensional Euclidean space with equilateral (=regular ?) exists only for $n\le 2$. For example the face-to-face angle of a regular tetrahedron is not of the form $2\pi/n$ for some natural number $n$. Hence you cannot find a desired regular tesselation. — Preceding unsigned comment added by HenrikRueping (talk • contribs) 14:41, 6 April 2011 (UTC)
- Ha, I was going to make the same comment. I think the tesselation desired here is the one associated to the affine Weyl group of type A_n. Perhaps I should be bold. 96.237.242.122 (talk) 12:52, 16 May 2014 (UTC)
Definition
editThe presentation of the formal definition does not fit so well with the first section, it seems that introducing apartments as Coxeter complexes here rather than in the next section would give a better idea of what a building is (together with examples), as is done in the informal presentation. This is what standard texts (at least Abramenko--Brwon) do. I would suggest including all 3 (?) definitions of a building in the "definition" section, and add an "examples" section before the fully developed section on spherical and affine buldings of SL_n (there should be mentioned right after the definition that a tree without leaves is a building).
Also, is the condition that all chambers be contained in at least 3 apartments (equivalent to the first condition in the current definition) not an additional one, called thickness? jraimbau (talk) 19:44, 19 December 2019 (UTC)