Ancient and Truly Original Brothers of the Silver Star
One of the eight orders of wizardry.
Again this appears to link to a name of one of the many competing secret and occult societies, which appear in Robert Anton Wilson and Robert Shea's Illuminatus! trilogy of novels.
Shea and Wilson, in their masterpiece trilogy dealing with paranoia and the nature of conspiracy theory, draw a world-picture of competing secret societies seeking to wrest control of the world from each other, whilst remaining obscure to established governments and the general public. (Sounds just like Unseen University in the pre-Ridcully days, doesn't it...)
The Argentum Astrum is apparently another name of the Consecrated Bavarian Seers, or the Illuminati.
However, it is also revealed that the real Illuminati just use the initials A.*.A, which deliberately are assigned no meaning: so that anyone coming along and confidently announcing that the "A.A." bit stands for "Argentum Astrum", or Silver Star, is immediately revealed as a fraud or a bluffer.
It should also be said that the Roundworld mystic, magician, and mountebank Aleister Crowley - not to be confused with Anthony Crowley - also set up a secret society called the Argentum Astrum, or Order of the Silver Star, in the early part of the 1900's, claiming that it had an unbroken pedigree going back as far as Ancient Egypt... for some reason, claims of longevity and continuity are readily accepted in the occult world and the usual burden of evidence is set aside...
To observers who have read and appreciated the Illuminatus! cycle, the thought occurs that Terry Pratchett cannot be unfamiliar with these books, as the Discworld novels are packed with sly allusions...