For group algebras $A=KG$ over a field $K$ with finite group $G$ there exists an outer product on Ext: $Ext_A^i(M,N) \otimes_K Ext_A^j(M',N') \rightarrow Ext_A^{i+j}(M \otimes_K M',N \otimes_K N')$.
Question:
Given a general finite dimensional algebra $A$ over a field $K$ with enveloping algebra $A^e=A^{op} \otimes_K A$, have such outer Ext-product of the form (for A-bimodules M,N,M',N'): $Ext_{A^e}^i(M,N) \otimes_K Ext_{A^e}^j(M',N') \rightarrow Ext_{A^e}^{i+j}(M \otimes_A M',N \otimes_A N')$
been studied with respect to existence and properties? Maybe there does not exist in general such a product with nice properties, but what if we assume more properties like N and N' being projective as one-sided modules or similar simplifications?
