th suzukiyuhei/slide_oberseminar.pdfexamples gimnamenable groups many minimal actbn gax mf c xrg...
TRANSCRIPT
Equivariant a - absaption theorem
for exact groups
'20Th Suzuki
June 30
(Hokkaido Universe)Based on arXiv i 2004.09461
Throughout the tak 、
ALWAYS ASSOME :
• Galgebias : United (nonze.ro)mostly Separatebe([email protected]
則れ幽 & Backgrounds
iii.𠠇ばiitCuntz
tf theory rigidiy.fm .. ..
Simple A .
旅に Expansion|_
Purely 州恌
km = ひ叫びk。 1が箭玔金 、
日興 Cuntz algebras REMEN
唎 ニ!a :姚明 は悠然で" Smallest
"
property in finite Edgewith (n - 1)は = 0
Examples Gimnamenable groups
Many minimal actbn GAXmf C Xr G Purely as Simple
(Law Spielberg , De Indes)③ Preserved unden
XrG for Outer actions
(kishim.to) etc. . .
Kinhberg-Phillips Classification theorem
Recall : Kircherg algebradet
separated Nuclear⇐) Simpletp.is 。
画 (Hrchberg 、 Phillips)ーーA.B
klrchbeigalgs.li・蔀 鼺、
Exms of klrchbegdgs (with UCT)
o Gntz algs On
L ・巤鷴蟣 a
they'sMainT.ee?:fIrststeptodevebpitsG-equivverdonfor exact groups
(e.g.Fn.SUm Z)に )
PNMSAIRealize kkA ,
- )as (asymptoms/
needto.makeltagmupr.nlce functor
to Elliott Intertwiningargument
Three Key ingradients on On(Hrchberg
'94)
① C 00220、 と uneSimple separatedNuclear
→ Neutral ize C (劄鼠認)② G A さ A KA Klubbeingt Accept to tread as
Note i -
" 0. C ZA)" 10が 1
③ ヨ DGO.ltD
sepexact.tt/omCA.B)nomtriuiFDIli+蠟Muchweakerre.rs/onofnuc1earityDxO-=Dxg-
T.daisd.ae GeqwVersion of these the
for exact countablegnupG
1三妣興 (a.k.a.bomdayamenat.ly)1型 (klrchberg-hi.semm)G i exact M - AG presents
G - Short exact sequences(E) はG : exact)金(Ozawa)[email protected]
に Space amenabih( ヨ Gで傑出に 竽が
E.×幽 . Amenable groups (trivial)
・ Knew groups G < GL(n. k)
( MEN Ki Held )- hyperbolic groups(GA 2Gamaable)
- MCGW- Out (En) -.- etc
Preserved by Extensions , increasing Unions、
amalgamatedfree.products 、
Background onNon commutatlvedyna.mu Systems
① Classification of
Get A
② Amenability of G n A
① G AA & Auth (for A simplyNaturally appear
in
Structure /Classification theory( constructin TYた!!!!!.
Classification of GTA : important
In What Sense ?
Obvious che conjugate」畿し纘)
But conjugate," to Strong !
Ex) が Z ~ AME UA)
で のな adu 。 x
たが断 の 女 が☆ Need to solve aboundary equation
wvがい,
in MAI to algebraic . . .
TimG : Infinitecountablegroupficountablegwupw.tnAP(eg amenable groups 蜃が で 間Pm 。gg 。。 附い_。
t.EE ftp.Nakamura : When G =4, they Only differ as before .
Fortunatery 、X and X"
Share important things .
. A Ya Z = AXのZ
- India the same
Action on Aw = ATA'
Right Identification :
Coqde conjugatey,
fois (Believed for lengthClassification of GA A requires
Lameinability of G .
Indeed tune for Waysestablished for aenable GClassification theorem
) 揃 factorComes , Jones 、 Ocneanu 、TheSaki
,
Sutherland,( katayama.kawahigashi.ir .Non -Classification results for non-amenable G
( Jones , M . Choda , Pope , . . .
,Brother -Vas ) (on Ru)
じ-alg casei Similar dkhot.myexpected( eg Izumi Conjecture )
Some clap Classification than : by many had
( Jones. Ocneanu.kishimc.to、 Nakamura,
IzumI , Matai .Sato , Szabo ,
. . .)
i We will SeeToday.. Common は
"
Ahis
is WRONG偲でしたが興りfor Edge In GOOD Way !
MinisterG : exact amenability
Then uptocoydeconjugacyit.pe condition
ヨ ! SG n G /pohtwiseouter.QAP.fm。ただし、𧑉:りた製品豔
Beyond anenable G
で 兜だな毖).pe la た 8 な憩が.irII Any condition in MT
doesn4 Follow from the otherto
Lie The equi v 02 - Him for exact groups
Mottathy results & Examples & questions .
豳 Gi exact
ヨ G n Q
02 XG = 02 Xr GL た。eamenabilig.lke conditions !
ffhhty 中Such actions
a?品感が岬を発)to Really E -algebraic
new phenomena 、
How to Witness amena唎 of GIA?Good Case : Xn = X
for s manyNota)鼠とし 、別
General Choice : not obvious
(In fact , the same is TRUE by My
Some Abstract formutation :
QAP (Quasi- Central Approximation Proper,Buss-Echteerhoffwilk.tt 49ヨ Sanare not of the
Father - t.pe Partition of UnityetYA)で
MTMTTA.AT Need a Slight reformutationvia ICA)
Roof : [email protected] Equivariant
N EKO)wny interacting argument△
'
Works 9
Lnice 0 : construct byOver Father setaveraging
Our situation : H Fiber sets
But with coefficients,
We haveniceaveraghgsl.itSome Fixed Point algebra are
Purely Infinite Simpleに呕→ Comes 's 2 × 2 trkk !!
We alsogetsGates results for!:鸝。鼠
QAPactbnsa.gekirdbergdgebns・ Appropriate Analogue of
02 - emb Ahn
Thanh You for Your attention !