Invariants of certain groups. I

  title={Invariants of certain groups. I},
  author={Takehiko Miyata},
  journal={Nagoya Mathematical Journal},
  • T. Miyata
  • Published 1 February 1971
  • Mathematics
  • Nagoya Mathematical Journal
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 v 1 , v 2 , · · ·, v n be a basis for V , then K is generated by v 1 , v 2 , · · ·, v n over k as a… 
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