When is a Surjective Comodule Endomorphism an Automorphism? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T00:50:23Z http://mathoverflow.net/feeds/question/105249 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/105249/when-is-a-surjective-comodule-endomorphism-an-automorphism When is a Surjective Comodule Endomorphism an Automorphism? Dyke Acland 2012-08-22T17:00:33Z 2012-08-22T17:28:08Z <p>Given a Hopf algebra $H$, a left $H$-comodule $V$, and a surjective comodule endomorphism $f: V \to V$. Can somebody give:</p> <p>(i) a set of neccessary, or sufficient, or both neccessary and sufficient, conditions for $f$ to have zero kernel?</p> <p>(ii) an example of such a comodule map with non-zero kernel?</p> <p>Thanks in advance guys</p>