Math 670
:
÷
pre
On
a
B to
The
'
.
9
Dyl
cpot, connected Lie
algebra
Cohomology
Th }
B
.
Papi
PPI
immediate
an
On
:
CCLG
a
We build up
Lenny
CCL 6
a
On
:
20
-
be
a
in
in
inv
so
Hug
'
"
a
a
u
.
cohomology to
is
whih
Hit
d
=
w
then
fm
Here
a
in
-
ihrritfns
isomorphic tnthe obvious way )
is
to the
de Rhem
:
bi
a
exact most be
is
.
i
,
Boland
gp
6
v :
then
,
-
hutton
inky
.
zero
.
Rg
at
in
in
°
du
a
is
din
are
'
-
'
guilt
van
.
,
volume
fm
not be bi ha
I
-
Rgoinv
mp
th
=
him
we
.
Roy
.
°
fm ,
Lg
=
wg
n
-
tom
ointke
:
WERY 6)
bi int
fe ,
-
Lyme we
"
4
=
Htwe
,
thhwg
=
K
.
,
9€
in
'
dw
"
=
HY dw
on
w
M
called
is
so he
mother
volume tom
a
dw=o
on
M
%
.
.
.
let wee N ( GM
be
Alike
men
wg
=L
,
? we
H
GEG
.
-
no
.
bi int 2-
,
dw
,
}Ly
to beg
'
'
hand
one
bi hot
D
by
is
=
LI
dl hkw
=
w
metro
leftist
my
v
=
an
,
6
in
or
u
vlg)=g
in
't
ii
{ lie themed
=
E
e
.
begun
6
→
inutwe
Now
W
she
fon
Lie
a
let
.
,
vote
}
'
,
afd
"
th
=
w
OPH
Bt th
hj
of
prgpsikb
following 2
=L Rgoinuhpwg
was
Lie gp 6 has
Evy
Sw
tom
fines
volg
'
v
in
but
gp
diffakl
she
,
M
the
fm
an
&
r46 )
we
Nw
N&
tom
Lie
since the
:
-
-
Tf
Df Tf
bi
:
6
Prof : ht
:
bi hit
Evy bi hit
:
c lord
euy
a
,
algebra
.
consignment
,
( CCL 6), the
sp
fry
an
6-
-
{ KY)
:
x to
}
:
thfn
3
ny
B
LI
bit nt
BI
.
Thin A C C L 6
6
:
Note : The
Prof let
be
vote fm
LI
a
multiplier deputy
4
so
,
astt
fm
vote
an
Rjsw
Sine
up
to
Nhi
Rg
Rhg
g
)
Haar
measure
bi
vote tom
A
in
-
.
£6
kg
w
.
Rgkw must be
,
here must be
&
LI
she
nonzero
mulhpkf
w
with
,
w
the
he
,
multiples
:
41g )
=
is
w=
& right mulhpli GHN comte
Sine left
the
knee
a
inched by this
mere
w
:
admits
4k$ Ulg ) Ulh)
hmonoohm
6→R←
B
=
4
so
Bt
're
he
a
6
she
Bt
Now
!
Nw 6
LAW
apt
is
,
5
,
Fully
:
d LI RYW
Now
I
is
=
=
,
4)
in
is
cohomology
B
w
-
it
so
,
KGGG
w
has
bi hut
a
.
For
eapk
{
=t÷oy
×
,
dw
:
idtw
to
Lapd RF =L ; RP dw
=
,
-
volume
th
vote
LI
the
so
,
o
=
,
Sine G
0
-
.
w
w
=
0
=
w
-
,
firm dwl
dvdgdudn
put
connected
,
subsp
f
,
& have
RI
also
is
w
IN
namely
BI
{ 13
.
18
.
5
so
Lay
so
.
wnmibd
D
w
the age
Also
LI Riw
closed
.
L :L
;
→
w
6
6→6
Rg :
&
ttg EG ; lihaie
,
are
hmotpr to the
Rgkw is cohomology to
w
.
is
cohomology to
w
,
so
5
&
w
are
www.g.us
.
Riwdwbdwkt
'Fi§×djo RI wdudgdvdn
algae
?,lja{
ME
"d"
via
Riwdvdgadudn
II op f.
"
↳ RY dvdgdvoh
5
,
.
who whys to
Define
,
=
LI
: 6
.
is
=
is
B
,
Lg
,
"
so
<
,
t.TN §×d5Rn←w
=
-
5
?
R
of
subsp
a
14) mist be the union
in
nutd
an
RY 6) he dnd
WE
bi hut
Liao
44)
W
& Lee
:
poofofpqf.tt
so
caput &
is
than Rgtw
ready
idwftg ,
,
A similar copvklm
shy
g
is
RI
&
here
BI
#
Remit
:
If
!1!
The
@
And
now
the
Pmfftht
If
o
w=
Prof
:
the
By
ref
WERYG )
=
Prop 1 ,
more
ey
than
is
=
w
comity 4
Siple
( bed
one
,
5
fm
BI
.
extnw denature
eat
&
BI
when F
=
them
th
is
IT DF
fthe
we
BI
angry process
Poffpgsjysppse
then
al
w
is
bi
'
'
wt
Bit by
.
.
for
w=dy
so
,
DJ
'
=
d
5
yes 'll 6) /
Some
w
earlier km
or
.
-
,
all bi
-
in
no
invoke
partial
A tens
aecbid
,
so
properties
w=dF=
o
.
.
B
:
is
colon hogs to
fm
in
a
9h
BI
a
Ass their
,
fon
,
so
differ
we
'll
world
be at lest
be
BI
one
& eat
BI
fm
& her
in
eth de Rhem cohaoloyobs
zero
by
Psp
2
#
.
.