50
M. L. RACINE
T 1+ M^ C M^
- v ( d )
.0 n (d3(^Q n ? ))"
Multiplying out and using the fact that M' C © while r 0, we obtain
the desired result s in both c a s e s .
LEMMA 17. Let H
q. e. d.
C l d 2
H.
H.
d . &Q ; v(
C ] L
) v ( c
3
) ; v f d ^ , v(d
2
) v f c ^ ; v ( d
3
) , v(d
4
) v(c
3
'). Le t
M„ = {H^AI A tt(&Af' $„), H i ? © . } . If we make the obvious identifications of
4 4 ' 4 0 4 4
M and M , determined by H and H as in Lemma 15, with subalgebras
of M , . then
4
^ r pr p ©
pr pr © ©
M'4
= I f f f f
r r r r
? ? ? ?
+ M' + M' where r = v(c ) - v(c ).
PROOF. It is eas y to se e that e + e (= unit element of M ) and
e ^ + e ^ (= unit element of M2)'
0
are contained in M„. Also a
r
„„-,' a
r[14
, „..,
3 3 4 4 4 [13] V
-1 -1 ~ v ( c i )
a, -,, a, , e M if and only if a g (c , c ) © = c © = ^p . We wish
to show that ©, c M' Let x
e
©. Since v(d, ), v(d
0
) v(c, ).
13 4 1 2 1 '
Previous Page Next Page