Building (mathematics)

In mathematics, a building (also Tits building, Bruhat–Tits building, named after François Bruhat and Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces. Initially introduced by Jacques Tits as a means to understand the structure of exceptional groups of Lie type, the theory has also been used to study the geometry and topology of homogeneous spaces of p-adic Lie groups and their discrete subgroups of symmetries, in the same way that trees have been used to study free groups.

Overview

The notion of a building was invented by Jacques Tits as a means of describing simple algebraic groups over an arbitrary field. Tits demonstrated how to every such group G one can associate a simplicial complex Δ = Δ(G) with an action of G, called the spherical building of G. The group G imposes very strong combinatorial regularity conditions on the complexes Δ that can arise in this fashion. By treating these conditions as axioms for a class of simplicial complexes, Tits arrived at his first definition of a building. A part of the data defining a building Δ is a Coxeter group W, which determines a highly symmetrical simplicial complex Σ = Σ(W,S), called the Coxeter complex. A building Δ is glued together from multiple copies of Σ, called its apartments, in a certain regular fashion. When W is a finite Coxeter group, the Coxeter complex is a topological sphere, and the corresponding buildings are said to be of spherical type. When W is an affine Weyl group, the Coxeter complex is a subdivision of the affine plane and one speaks of affine, or Euclidean, buildings. An affine building of type is the same as an infinite tree without terminal vertices.

Building (disambiguation)

A building is a constructed object intended for occupancy by humans or animals.

Building may also refer to:

See also

Online creation

Online creation, also referred to as OLC, online coding, online building, and online editing, is a software feature of MUDs that allows users to edit a virtual world from within the game itself. In the absence of online creation, content is created in a text editor or level editor, and the program generally requires a restart in order to implement the changes.

Online creation as original content

An aspect of online creation that separates it from "mere game play" is that online creation systems can generally be used to create new content — new objects, new locations, new creatures — rather than simply creating instances of predefined items in the game world. Some have observed that certain forms of online creation — notably those associated with creating new commands — can threaten the stability of the server.

History

Origins

The first publicly available MUD that featured in-game creation of the game world was Skrenta's 1988 Monster.

Passion (Kreesha Turner album)

Passion is the first album by the Canadian singer Kreesha Turner. It was released on August 12, 2008, in Canada and was released in early 2009 in the United States.Passion had been available for advanced streaming on MuchMusic.com. a week earlier.Passion was released in the US in early 2009.

In early August, 2008, the album was leaked onto MTV Canada's The Leak on its official website.

Initially, on the back of the album, track 14 was listed as the "Bounce With Me (Rhythm Mix)" but this was an error and the track is actually the "Don't Call Me Baby (Rhythm Mix)". This error on the back cover was corrected on later pressings of the album.

Although Turner originally signed in the US to Virgin Records, a Capitol Music Group label, her first American release will instead be shifted to the Capitol Records imprint, also within the Capitol Music Group umbrella. This will keep a consistency with her Canadian releases under EMI Music Canada which utilize the Capitol Records imprint and are copyrighted by Capitol Records, LLC.

Talk (Paul Kelly album)

Talk is the debut album by Australian rock group Paul Kelly and the Dots and was originally released on 30 March 1981 by Mushroom Records and re-released in 1990.Jo Jo Zep & The Falcons leader Joe Camilleri produced seven of the eleven tracks with three tracks produced by Martin Armiger (The Sports) and one by Trevor Lucas (ex-Fairport Convention, Fotheringay). The album spawned the singles, "Recognition", "Billy Baxter" and "Lowdown". Only "Billy Baxter" appeared on the Kent Music Report Singles Chart it peaked at No. 38. The album peaked at No. 44 on the related Albums Chart. All tracks were written by Kelly, including two co-written with guitarist Chris Langman.

Background

Paul Kelly and the Dots had formed in August 1978 in Melbourne from the remains of High Rise Bombers, which included Martin Armiger. Their debut single "Recognition" was issued in 1979, under the name The Dots, on an independent label, but had no chart success. "Recognition" line-up were Kelly (vocals), Chris Langman (guitars), Chris Worrall (guitars), Paul Gadsby (bass guitar) and John Lloyd (drums). The version of "Recognition" included on Talk is not the single version, but a re-recording.

1982–1992

1982–1992 may refer to: