Singularities, Monodromy and Zeta Functions Blatt 8
Exercises for discussion in the exercise class on 13.12.2018
Aufgabe 1:
Letϕ:K[x1, ..., xn],→Dnbe the natural embedding of the polynomial ringK[x]into the Weyl algebraDn ⊆ EndK(K[x]).
Prove that, for anyi∈ {1, ..., n} andg∈K[x],
[∂i, ϕ(g)] =ϕ
∂g
∂xi
.
Aufgabe 2:
LetK be a field and consider the vector spaceKω. Letxand∂ operate onKωwith x(ai)i∈ω= (0, a0, a1, ...)
and
∂(ai)i∈ω= (a1,2a2,3a3, ...).
Show that theK-sub-algebra ofEndK(Kω)generated byxand∂ is isomorphic toD1(K).
Course website:http://reh.math.uni-duesseldorf.de/~internet/Zeta_WS18/
