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Let G be a group and let k be a field. A K-representation ρ of G is a homomorphism of G into the group of non-singular linear transformations of some finite-dimensional vector space V over k. Let K be the field of fractions of the symmetric algebra S(V) of V, then G acts naturally on K as k-automorphisms. There is a natural inclusion map V→K, so we view V as a k-subvector space of K. Let v1, v2 , · · ·, vn be a basis for V, then K is generated by v1, v2 , · · ·, vn over k as a field and thesedoi:10.1017/s0027763000014069 fatcat:nsj6fifujncjjaj3m2dstrtqzy