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 />
A closed symmetric monoidal category<br />
Adjoint functors and a spectral sequence<br />
Two categorical constructions<br />
Hochschild cohomology<br />
Example: Hochschild cohomology of a poset<br />
Let P be a poset. We have HH ∗ (kP) ∼ = H ∗ (P; k)<br />
(Gerstenhaber-Shack). When P = x α →y, the triple<br />
τ : F (P) → P e becomes<br />
(α,1 x )<br />
<br />
[1 x ]<br />
[α] (y, x)<br />
<br />
<br />
(1 y ,α)<br />
<br />
[1 y ]<br />
(α,1 op<br />
x )<br />
<br />
(x, x)<br />
<br />
(1 x ,α op )<br />
(1 y ,α op )<br />
(α,1 op<br />
y )<br />
<br />
(x, y)<br />
Note that<br />
kP(x, x) = k1 x , kP(y, y) = k1 y , kP(y, x) = kα and<br />
kP(x, y) = 0. Moreover Res τ kP = kP ∼ = k.<br />
Fei Xu Finite category algebras<br />
(y, y)