# Injective modules over Fourier algebra

Is there any article on injective modules over Fourier Algebras? Do we have anything about injectivity of $A(G)$ as a $A(G)$-bimodule?

• This is essentially the same as mathoverflow.net/questions/99345/… Let me repeat my comment from that version of the question: Not to my knowledge. (You probably want to be working in the cb-category, of course.) – Yemon Choi Jun 20 '12 at 4:27
• I should also add that I am reasonably in touch with these matters, and have looked on MathSciNet, so while it is possible that someone has written a paper on this that I don't know of, I must immodestly say that it is unlikely. – Yemon Choi Jun 20 '12 at 4:28
• But for example we know that $L^1(G)$ is injective as a left $L^1(G)$-module if and only if $G$ be discrete and amenable. So this question came to my mind that what append for $A(G)$. – Zora Jun 20 '12 at 6:32
• Is it if and only if? Or just we can say that if G is compact then A(G) is injective as an $A(G)$-bimodule. Would you please explain "dual os-bimodules over it are os-injective (and all one-sided os-modules are os-injective)" more or suggest me a reference? I believe that it is not useless to investigate the injectivity of modules over $A(G)$ since biinjectivity is related to biflatness. Anyway sometimes I ask silly questions. But at the moment I guess that it is not that silly. – Zora Jun 20 '12 at 8:57
• I closed the older version as a duplicate - mathoverflow.net/questions/99345/… - the closing votes on this one will clear in a few days... – François G. Dorais Jun 20 '12 at 15:29