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Outline Definitions and examples Homological properties of kC-mod An example Infinitely generated HH ∗ The ordinary cohomology ring is infinitely generated and has no nilpotents. Thus HH ∗ (kE) is not finitely generated either, even modulo nilpotents. This calculation is very similar to that of the Hochschild cohomology ring of a Koszul algebra. In fact, kE is Koszul. Let A be a Koszul algebra and r its radical. Then the image of the following canonical map Ext ∗ −⊗ Ae(A, A) A A/r Ext ∗ A(A/r, A/r) is exactly the (graded) center. Snashall constructed Koszul algebras with infinitely generated Hochschild cohomology rings (modulo nilpotents) independent Fei Xuof the Finitechoice category algebras of a base field.
Compatibility Outline Definitions and examples Homological properties of kC-mod An example There exists a commutative diagram Ext ∗ kE e(kE, kE) −⊗ kE k −⊗ kE kE/r Ext ∗ kE(k, k) Ext ∗ kE(kE/r, kE/r). − ˆ⊗kE/r Fei Xu Finite category algebras
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