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 P: 57 Hello, I think I have an idea of what graded algebra means but when people say it has Z_2 grading etc I'm puzzled. Could someone please help me out? By 'Z' I mean integers and '_2' means mod 2.
 Emeritus Sci Advisor PF Gold P: 16,101 Normally, when you think of a graded algebra, you imagine each nonzero element being assigned a natural number as its degree. But there's no reason to restrict ourselves to using the natural numbers. A Z2-graded algebra is one where the degree is an element of Z2. For example, C is a Z2-graded algebra over R. The "even" elements (degree 0) of C are the purely real numbers, and the "odd" elements (degree 1) of C are the purely imaginary numbers. Exercise: check that this really is a grading. For example, i is homogenous, and in the equation i * i = -1 we see that the degrees match: the degree of i * i should be 1 + 1 = 0 (remember, they're elements of Z2), and the degree of -1 is, in fact, 0. See Wikipedia for more info.
 P: 57 I see, thank you for that information. The example I have here is tensor algebra which it says has Z_2 grading. So I guess Z_2 grading divides tensor algebra into T+ and T- where elements of T+ has even degrees(including 0) and elements of T- has odd degrees? Now I'm thinking if any other grading would be possible? In other words grading is not unique? Is it? or it isn't? p.s. I referred to wikipedia first but it didn't explain Z_2 grading :D
Emeritus
PF Gold
P: 16,101