I can not understand a paragraph of this book:
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The grading is just the degree of the polynomials in the usual sense.

Daniel McLaury
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can you write it in more detailes? – Mar 13 '16 at 18:33
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why they are homogenous of degree 2? – Mar 13 '16 at 18:34
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$q$ is just a number (well, an element of $k$). So $x y - q y x$ is a homogeneous second degree polynomial. – Daniel McLaury Mar 13 '16 at 18:36