Indefinite Form
There are as many as eight different double covers of O(p, q), for p, q ≠ 0, which correspond to the extensions of the center (which is either C2 × C2 or C4) by C2. Only two of them are pin groups—those that admit the Clifford algebra as a representation. They are called Pin(p, q) and Pin(q, p) respectively.
Read more about this topic: Pin Group
Famous quotes containing the words indefinite and/or form:
“There are times when they seem so small! And then again, although they never seem large, there is a vastness behind them, a past of indefinite complexity and marvel, an amazing power of absorbing and assimilating, which forces one to suspect some power in the race so different from our own that one cannot understand that power. And ... whatever doubts or vexations one has in Japan, it is only necessary to ask oneself: “Well, who are the best people to live with?””
—Lafcadio Hearn (1850–1904)
“Upon the whole, necessity is something, that exists in the mind, not in objects; nor is it possible for us ever to form the most distant idea of it, consider’d as a quality in bodies. Either we have no idea of necessity, or necessity is nothing but that determination of thought to pass from cause to effects and effects to causes, according to their experienc’d union.”
—David Hume (1711–1776)