my beamer presentation - Departament de matemà tiques
my beamer presentation - Departament de matemà tiques
my beamer presentation - Departament de matemà tiques
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Outline<br />
Definitions and examples<br />
Homological properties of kC-mod<br />
An example<br />
Infinitely generated HH ∗<br />
The ordinary cohomology ring is infinitely<br />
generated and has no nilpotents. Thus HH ∗ (kE) is<br />
not finitely generated either, even modulo nilpotents.<br />
This calculation is very similar to that of the Hochschild<br />
cohomology ring of a Koszul algebra. In fact, kE is<br />
Koszul.<br />
Let A be a Koszul algebra and r its radical. Then the<br />
image of the following canonical map<br />
Ext ∗ −⊗<br />
Ae(A, A)<br />
A A/r<br />
Ext ∗ A(A/r, A/r)<br />
is exactly the (gra<strong>de</strong>d) center.<br />
Snashall constructed Koszul algebras with infinitely<br />
generated Hochschild cohomology rings (modulo<br />
nilpotents) in<strong>de</strong>pen<strong>de</strong>nt Fei Xuof the Finitechoice category algebras of a base field.
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