Unformatted text preview: make use of it, through the identity (3.5.2.3). (3.5.3) Because our proof of (3.5.0.3) in the general case is so unen lightening we first present the proof in the case b = 2, which is somewhat more intelligible. The assertion to be verified is Lie (p)k I (P  Q) Lie (Q)e (~ (r (l) ^ z (2))) k+g'=p 1 (3.5.3.0)  I (P p Qp)(o~ (z (1) ^ z (2)))  o~ (I (P  Q) (, (1) ^ z (2))) modulo dF(V, (gv). Substituting via (3,5.1.1) and noting that by (3.5.1.3) the terms under the summation sign vanish for (~0, (3.5.3.0) becomes Lie (P)Px (I (P  Q))(~r (1) ^ a (2))  I(Pp  QO)(a (1) ^ a (2)) (3.5.3.1)  ~~(I(P Q)(,(I) ^ ,(2))) modulo dF(V, (9~,). Expanding the interior products and substituting via (3.5.1), (3.5.3.1) becomes Lie (P)P1 (f(1) a (2)  f(2) a (1))  (h (1) a (2)  h (2) a (1)) (3.5.3.2)  ~(g(1)z(2)g(2)z(1))modulodr(V, Cv). 4*...
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This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.
 Fall '11
 NormanKatz

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