Timeline for Surjectivity of Invariants

7 events

when toggle format	what		by	license	comment
Mar 20, 2012 at 8:41	vote	accept	mark
Mar 20, 2012 at 1:47	history	edited	Ralph	CC BY-SA 3.0	slight simplification
Mar 20, 2012 at 1:45	comment	added	Ralph		I don't know, if there is such a characterization ($W$ $k$-free is sufficient, probably also $W$ $k$-projective). And thanks for pointing out the correct order of the Reynolds operator.
Mar 19, 2012 at 19:44	comment	added	Mark Wildon		@Ralph Your argument shows, still more generally, that if $U$ is a submodule of $V$ with quotient module $V/U \cong W$ then there is a $k$-algebra homomorphism $k[V] \rightarrow k[W]$ that preserves degrees and invariants. Is there any characterization of when the induced map $k[V]^G \rightarrow k[W]^G$ is surjective? (One small typo: the Reynolds averaging operator sends $k[V]^H$ to $k[V]^G$ for $H \le G$.)
Mar 19, 2012 at 15:50	comment	added	Ralph		Added: $r$ is degree-preserving. For let $u,w$ be monomials such that $r(u \otimes w) \neq 0$. Then $\deg u = 0$ and $\deg r(u \otimes w) = \deg(u \cdot w) = \deg w = \deg w + \deg u = \deg(w \otimes u)$.
Mar 19, 2012 at 15:27	history	edited	Ralph	CC BY-SA 3.0	added 13 characters in body
Mar 19, 2012 at 15:20	history	answered	Ralph	CC BY-SA 3.0