This is a /v/ related article, which we tolerate because it's relevant and/or popular on /tg/... or we just can't be bothered to delete it.
Centauri α is the brightest star in the constellation of Centaurus. It is a binary star system, the third brightest star in the night sky, and the extrasolar star closest to our own. It's a popular destination in near-future space RPGs.
But you're here because of the vidya gaem "Sid Mier's Alpha Centauri" (SMAC), which is not only a strategy game accepted and welcome on /tg/, but the faction leaders in the game are also a meme used in mild role-playing.
It's the spiritual successor to Civilization 2, and direct predecessor to Civilization 3 since it shares much of of the same dev team. One of the possible ending conditions of the Civilization games is to launch the first colony ship into space -- destination Alpha Centauri. Once they find a habitable planet, the team leaders suffer a political breakdown, culminating in the assassination of the colony ship's captain. Each team leader takes a part of the colony ship and some of the colonists in hibernation, and make planetfall. The game starts with your faction arriving, reviving the colonists for labour, and exploring the new world.
There will never be a sequel to Alpha Centauri because the intellectual property rights are a clusterfuck.
The Roleplaying Game
Steve Jackson Games made a GURPS sourcebook for Sid Mier's Alpha Centauri. The cover has a white border, which is unusual for GURPS splatbooks. You can usually find a scan of this book in 4chan's rapidshares catalog.
The Factions
The elegan/tg/entlefolk, fa/tg/uys and ca/tg/irls will sometimes post to a thread with one of the faction leader portraits and respond in-character for that faction leader. This should help you understand what the fuck they're on about.
Gaia's Stepdaughters
Leader: Lady Dierdre Skye (Scottish)
Pacifist, Explorers, Green agenda, hates Free Market
Hippy-dippy freak. Wants to integrate with the existing biology, including the mind-raping local fauna.
Human Hive
Leader: Chairman Sheng-Ji Yang (Chinese)
Aggressive, Conquerers/Builders, Police State agenda, hates Democracy
Socialist TO THE EXXXTREME, all about everyone being equal and subservient to the whole, even if it requires brain stapling for the greater good. Everyone lives underground.
Morgan is all about having huge wealth, and making sure his citizens live in luxury. If that means the environment gets fucked up beyond recognition, or other factions have to live in poverty, so be it.
Peacekeeping Forces
Leader: Commissioner Pravin Lal (India)
Erratic, no specialists, Democracy agenda, hates Police State
Wuss; usually the first to get wiped out in a game. When role-playing in a thread, Pravin will usually say something about "why don't we come to some sort of agreement" and everyone else agrees that Pravin should shut the fuck up.
Spartan Federation
Leader: Colonel Corazón Santiago (Puerto Rico)
Erratic, Discoverers/Conquerers, Power agenda, hates Wealth
Will kick your ass. Has plus-four strength. All about military power and how soldiers are superior to soft lazy civvies like you. Most often accused of assassinating the colony ship's captain, despite a complete lack of proof.
Techno-fetish nerd, with all the toys (all of them), thus beloved of the denizens of /tg/ and /v/. He and Miriam fight like cats and dogs -- if only they'd finally get a room and fuck, but she's an ugly bitch and he's a unwashed dweeb.