Invariants of Certain Groups I
Keyword(s):
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 these are algebraically independent over k, that is, K is a rational field over k with the transcendence degree n. All elements of K fixed by G form a subfield of K. We denote this subfield by KG.
1985 ◽
Vol 28
(3)
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pp. 319-331
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1993 ◽
Vol 45
(2)
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pp. 357-368
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1990 ◽
Vol 49
(3)
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pp. 399-417
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1982 ◽
Vol 25
(2)
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pp. 133-139
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1986 ◽
Vol 69
(4)
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pp. 37-46
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