Invariant Ideals in Split Hopf Algebroids - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T21:26:53Z http://mathoverflow.net/feeds/question/101248 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/101248/invariant-ideals-in-split-hopf-algebroids Invariant Ideals in Split Hopf Algebroids Jon Beardsley 2012-07-03T18:04:44Z 2012-07-03T18:52:47Z <p>Given a split Hopf algebroid $(S,\Sigma)=(S,S\otimes B)$ over $K$, Ravenel leaves as an exercise the proof of the following:</p> <p>An ideal $J\subset S$ is invariant under the action of the group $\mathrm{Hom}(B,K)$ if and only if $\eta_R(J)\subset J\Sigma$, where $\eta_R$ is the right unit.</p> <p>Is it clear where the group action of $\mathrm{Hom}(B,K)$ on $S$ or $J$ comes from? Obviously, by the fact that the algebroid is split, there is an action of $\mathrm{Hom}(B,K)$ on $\mathrm{Hom}(S,K)$. </p>