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By Rotman J.J.

ISBN-10: 0821847414

ISBN-13: 9780821847411

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Example text

Ic) c. 6 S - I A 1 die Beisplelen Oresche (vgl. als Algebra ein. 2 zu d e n Quotientenring und yon Darstellung GegenstGck wir Diese es : definierte ein Verhalten Situation A[~] 2' auf k. spielen. S-I(A[g] 8 ) Dabel ~ber Koeffizientenringes In d e r Oresch Weyl-Algebra Eolle kurz 38- nun b = typlsches Element yon B = S-IAU(~) so gibt es fiir d e n fNr Fall Induktion. aIEA 4-5 die c. i (so d a b s-lai folgenden A[X]D Satz: Eine Lie Dann ist die Men~e und A und gewidmet, P ~--+PC~A so Dies mit den der wurde n dutch Elementen B = S - I ( A [ g ] ~).

A H(P). 6) und deshalb auch in der Algebra A@kK , den Fall A p = 0 ist Oresch in wie man leieht aus der -27- Tatsache sehliebt, mit yon dieser letzten direkt braucht. 6) K und der obigen Uberlegung, Bijektion steht (vermSge gen~gt deshalb, es zu b e t r a c h t e n , zu Q(A) H @ kK - indem man nichts mit Satz zu sein K' ~ jedes Spec A = Q(A) man b e a e h t e , £ndert). = H(p) A @ k K = A @ H(H @ k K) 0 Q(A) @ k K dab Die mit K im allgemeinen A - Durchschnitt dab die K'. P~--*P ~ (A @ kK)). 10.

X n, verifizieren N----+ A. wollen, aAb beweist die muS. a® b k6nnen w~hlen. 1: etwa tragen. ein gilt Ideal, yon - Untermoduln deswegen da~ enthglt, bzw. = U ( g ) @ a2] ) = [ x ' a l ] Seien Nach des - Untermodul ~A [g,~] Insbesondere Beweis I ~ U ~ operiert und das heist Struktur : im ist, Nullteiler auch -- [[y,x], m] ÷ [x,[y,m]] folgt. Zweiter 52- Das = O. den Das Satz. ~.. Xnb wobei Y 6 ~. endliche ~ Untermodul # 0 (einen = (x I - y ) a x 2 . . X n b Qed. - Moduln von M@ (~ cN. "zerlegbaren auflSsbare Enth~it Tensor"), L Lie ~berhaupt dann auch - eines, bei dem Beweis: a und durch I.

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Advanced algebra by Rotman J.J.


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