Mnthbtoibgefotnilht
in
proof of the
ar
Mi
is
diffaft
a
or
This
thy
quidntf
,
is
the
:
let
:
The
Mere
.
Sd
an
-
subtly
:
:
6
}
)
H
→
↳
wtd
g
→
.
4
homomorphism
.
6→H
:
; it mf
deputed
4
on
'
17
:
gt
→
h
→
.
:
sipf annwff Tf
Y : gosh
.
B
Lie ab
a
F
hmomorphm then
.
'
.
Lie
,
gp
.
han
h
.
It
&
essutl
is
wi
theorem
G
gently
tht the idal I
the lie gp
an
G
have Boworphz Lie algebra then
,
&
H
Bonophz
are
.
:
idnlil Lie abeks
) he
San
:
TP
-
mphm d 4 : g
4
Lie gps 6
hypothesis
Wi
fkwy
4=4
d
.
theft
,
all
homo
.
the
Png
st
connected
) &
an
in
a
6 & It be Lie
gps
shpf
sipf
go
§
If
He Lie
on
key point
4
lot
,
IF Yt
=
Gal d-
didn't
ideal
them
pwos
th
an
they're
not
isomorphic
he
as
low
gps
em
)
homo morphs
.
:
& 5412 )
he isaorph
Lie
a
books
tgh
em
they're
ht
isomgphz
Liegps
as
lnrem
homwmorphif
,
To
see
SDG )
th read tht
Suk )
Now for
)a#
alt
Ditttte
:
hshte @
tot
:
a a)
E-
o
the
tot
she
sermon minus }
-
the identity
let
:
d.
{ ( 9£
Fo )
Ey
=
HHSNX
sit
: x. ,
aid
.
=
,zelR}
1
'
T
)
.
.
Then
at He
Sun
)
H
t
so
,
too )
T
IHF
)
at
+
;
C :;)
so
3×3
nets to
=
#
{
=
=
'
a co
)
nots to the idnlif
four I real ) diners it
I
so
,
=
we
det
=
#
l ::)
+
al
o
) a'toTT=
skew Humility
a
=
an
It )
an
H)
6) It:)
Of
.
.
need another and ith
alt )
2
'
-
.
course
Of
azilt
case
)
d,
+
1 oil
'
Its
=
Ilo )
+
atot
,
,
,
It )
the space
of
2×2 skew Hemi tin
that odith shed
-
cane
minus
fan different Hy
B
.
9¥
At
to
aittlanlt )
o=
:
L
, ,
1 01=1
,
an
ta
,,
Hai
we
,
sum
tht
see
Suk )
Nn
the
dan
B
tht
5013 )
It )
101=0,4 101=0
0=2510 ) tazzlo )
So th
,
±
=
,
-
as Hartt )
an
10=1
aultlaidtt
-
,
get
So
,
.
B
the set of skew Homihh treeless 2×2 minus
,
-
ID
{ ( Izi
SUK)
Dfni 9 :
.
,
ztc }
R,
re
:
so
B)
-
.
Suk ) by
oID-sExinxeifisthm.ifAiEtItg.YD.BifEzIITD.wehey.wyzHitxzzixHidca.BD-uEmidiaiiYzixjxtkp-kfiy.YIIzIiiYxizixiHitxnexniiIecuH.u.D.tatExiim.xIIYiltxtitiizxitiilDtxIihxitImtx2itiixitItIDC2x.yz-2x2yyikYit2t2Y22DtiC2xzz.2x.aDit4f12y.zz-2ygDtil2xzzi-2x.zD-kx.yz-2xzyDiJpfSoThBrdfBaL.ealg.BowphsHonogeneoySThmhtHkaobndsbgpfaliegpGl6t4HbethesetfkttcsebEsH.gEG3.TfitiGos4Histhenetlprjutm.thn4Hhesawynmfds1wlest.0tTBsnooth8@ZloalseAsf4HitrgHe4H.FnhlUfgHCasnrthpriWes6s.t
the
proof
,
apain
}
we
so
ship it
.
Mntldsfthefom 4H
are
albd tongues
spaces
.
Mere
gulf
,
suppose
a
lie
gp
6 aeb
on
a
afd M
;
i.e.
,
7
z
:
6xM→M
st
,
.
.
m
He,
D=
smooth
x
V.
saidlw
to
.
.
,
xtm
imlgh
D= nlg , ylh xD ttghtb
loftrwrik g. x try 1g D)
,
,
,
,
XEM
The aelm
For
is
xe
my
tnsitne
called
M
,
the
isotropy
if
t Y
y EM
subgrp
( Mti npotw Hit west the
,
,
,
of
7
g
b at
isotropy
EG
x
st
.
the
is
repeat ath
g
.
x=y
.
{
grp G×= GEG
6×→ Ant ( Tx M )
g
to
dgxltxm
:
gx
=D
.