Unitary conjugacy for type III subfactors and W*-superrigidity

[1] Boutonnet, R.: W -superrigidity of mixing Gaussian actions of rigid groups. Adv. Math. 244,

69–90 (2013) Zbl 1288.46036 MR 3077866

[2] Boutonnet, R., Houdayer, C.: Amenable absorption in amalgamated free product von Neumann algebras. Kyoto J. Math. 58, 583–593 (2018) Zbl 1406.46045 MR 3843391

[3] Boutonnet, R., Houdayer, C., Vaes, S.: Strong solidity of free Araki–Woods factors. Amer. J.

Math. 140, 1231–1252 (2018) Zbl 1458.46050 MR 3862063

[4] Brothier, A., Deprez, T., Vaes, S.: Rigidity for von Neumann algebras given by locally compact

groups and their crossed products. Comm. Math. Phys. 361, 81–125 (2018) Zbl 1403.46053

MR 3825936

[5] Brown, N. P., Ozawa, N.: C  -algebras and Finite-Dimensional Approximations. Grad. Stud.

Math. 88, Amer. Math. Soc., Providence, RI (2008) Zbl 1160.46001 MR 2391387

[6] Caspers, M.: Gradient forms and strong solidity of free quantum groups. Math. Ann. 379,

271–324 (2021) Zbl 07307510 MR 4211088

[7] Chifan, I., Houdayer, C.: Bass–Serre rigidity results in von Neumann algebras. Duke Math. J.

153, 23–54 (2010) Zbl 1201.46057 MR 2641939

A Self-archived copy in

Kyoto University Research Information Repository

https://repository.kulib.kyoto-u.ac.jp

Unitary conjugacy for type III subfactors and W -superrigidity

1719

[8] Chifan, I., Ioana, A., Kida, Y.: W  -superrigidity for arbitrary actions of central quotients of

braid groups. Math. Ann. 361, 563–582 (2015) Zbl 1367.20033 MR 3319541

[9] Chifan, I., Popa, S., Sizemore, J. O.: Some OE- and W  -rigidity results for actions by wreath

product groups. J. Funct. Anal. 263, 3422–3448 (2012) Zbl 1304.37006 MR 2984072

[10] Chifan, I., Sinclair, T.: On the structural theory of II1 factors of negatively curved groups.

Ann. Sci. École Norm. Sup. (4) 46, 1–33 (2013) (2013) Zbl 1290.46053 MR 3087388

[11] Connes, A.: Une classification des facteurs de type III. Ann. Sci. École Norm. Sup. (4) 6,

133–252 (1973) Zbl 0274.46050 MR 341115

[12] Fang, J., Smith, R. R., White, S.: Groupoid normalisers of tensor products: infinite von Neumann algebras. J. Operator Theory 69, 545–570 (2013) Zbl 1289.46088 MR 3053355

[13] Haagerup, U.: Operator-valued weights in von Neumann algebras. I. J. Funct. Anal. 32, 175–

206 (1979) Zbl 0426.46046 MR 534673

[14] Haagerup, U.: Operator-valued weights in von Neumann algebras. II. J. Funct. Anal. 33, 339–

361 (1979) Zbl 0426.46047 MR 549119

[15] Houdayer, C., Isono, Y.: Unique prime factorization and bicentralizer problem for a class of

type III factors. Adv. Math. 305, 402–455 (2017) Zbl 1371.46050 MR 3570140

[16] Houdayer, C., Isono, Y.: Factoriality, Connes’ type III invariants and fullness of amalgamated

free product von Neumann algebras. Proc. Roy. Soc. Edinburgh Sect. A 150, 1495–1532

(2020) Zbl 1452.46046 MR 4091070

[17] Houdayer, C., Popa, S., Vaes, S.: A class of groups for which every action is W -superrigid.

Groups Geom. Dynam. 7, 577–590 (2013) Zbl 1314.46072 MR 3095710

[18] Houdayer, C., Ricard, É.: Approximation properties and absence of Cartan subalgebra for free

Araki–Woods factors. Adv. Math. 228, 764–802 (2011) Zbl 1267.46071 MR 2822210

[19] Houdayer, C., Shlyakhtenko, D., Vaes, S.: Classification of a family of non-almost-periodic

free Araki–Woods factors. J. Eur. Math. Soc. 21, 3113–3142 (2019) Zbl 1434.46037

MR 3994101

[20] Houdayer, C., Trom, B.: Structure of extensions of free Araki–Woods factors. Ann. Inst.

Fourier (Grenoble) (to appear)

[21] Houdayer, C., Ueda, Y.: Rigidity of free product von Neumann algebras. Compos. Math. 152,

2461–2492 (2016) Zbl 1379.46046 MR 3594283

[22] Houdayer, C., Vaes, S.: Type III factors with unique Cartan decomposition. J. Math. Pures

Appl. (9) 100, 564–590 (2013) Zbl 1291.46052 MR 3102166

[23] Ioana, A.: Rigidity results for wreath product II1 factors. J. Funct. Anal. 252, 763–791 (2007)

Zbl 1134.46041 MR 2360936

[24] Ioana, A.: W  -superrigidity for Bernoulli actions of property (T) groups. J. Amer. Math. Soc.

24, 1175–1226 (2011) Zbl 1236.46054 MR 2813341

[25] Ioana, A.: Cartan subalgebras of amalgamated free product II1 factors. Ann. Sci. École Norm.

Sup. (4) 48, 71–130 (2015) Zbl 1351.46058 MR 3335839

[26] Ioana, A.: Rigidity for von Neumann algebras. In: Proc. International Congress of Mathematicians (Rio de Janeiro, 2018), Vol. III, World Sci., Hackensack, NJ, 1639–1672 (2018)

Zbl 1461.46058 MR 3966823

[27] Ioana, A., Peterson, J., Popa, S.: Amalgamated free products of weakly rigid factors and calculation of their symmetry groups. Acta Math. 200, 85–153 (2008) Zbl 1149.46047

MR 2386109

A Self-archived copy in

Kyoto University Research Information Repository

https://repository.kulib.kyoto-u.ac.jp

Y. Isono

1720

[28] Isono, Y.: Some prime factorization results for free quantum group factors. J. Reine Angew.

Math. 722, 215–250 (2017) Zbl 1445.46044 MR 3589353

[29] Isono, Y.: Unique prime factorization for infinite tensor product factors. J. Funct. Anal. 276,

2245–2278 (2019) Zbl 1418.46027 MR 3912805

[30] Izumi, M., Longo, R., Popa, S.: A Galois correspondence for compact groups of automorphisms of von Neumann algebras with a generalization to Kac algebras. J. Funct. Anal. 155,

25–63 (1998) Zbl 0915.46051 MR 1622812 (1998).

[31] Kosaki, H.: Extension of Jones’ theory on index to arbitrary factors. J. Funct. Anal. 66, 123–

140 (1986) Zbl 0607.46034 MR 829381

[32] Marrakchi, A.: Solidity of type III Bernoulli crossed products. Comm. Math. Phys. 350, 897–

916 (2017) Zbl 1371.46056 MR 3607465

[33] Ozawa, N., Popa, S.: On a class of II1 factors with at most one Cartan subalgebra. Ann. of

Math. (2) 172, 713–749 (2010) Zbl 1201.46054 MR 2680430

[34] Peterson, J.: Examples of group actions which are virtually W -superrigid. arXiv:1002.1745

(2010)

[35] Popa, S.: On a class of type II1 factors with Betti numbers invariants. Ann. of Math. (2) 163,

809–899 (2006) Zbl 1120.46045 MR 2215135

[36] Popa, S.: Some rigidity results for non-commutative Bernoulli shifts. J. Funct. Anal. 230,

273–328 (2006) Zbl 1097.46045 MR 2186215

[37] Popa, S.: Strong rigidity of II1 factors arising from malleable actions of w-rigid groups. I.

Invent. Math. 165, 369–408 (2006) Zbl 1120.46043 MR 2231961

[38] Popa, S.: Strong rigidity of II1 factors arising from malleable actions of w-rigid groups. II.

Invent. Math. 165, 409–451 (2006) Zbl 1120.46044 MR 2231962

[39] Popa, S.: Cocycle and orbit equivalence superrigidity for malleable actions of w-rigid groups.

Invent. Math. 170, 243–295 (2007) Zbl 1131.46040 MR 2342637

[40] Popa, S.: Deformation and rigidity for group actions and von Neumann algebras. In: International Congress of Mathematicians (Madrid, 2006), Vol. I, Eur. Math. Soc., Zürich, 445–477

(2007) Zbl 1132.46038 MR 2334200

[41] Popa, S.: On the superrigidity of malleable actions with spectral gap. J. Amer. Math. Soc. 21,

981–1000 (2008) Zbl 1222.46048 MR 2425177

[42] Popa, S., Vaes, S.: Group measure space decomposition of II1 factors and W  -superrigidity.

Invent. Math. 182, 371–417 (2010) Zbl 1238.46052 MR 2729271

[43] Popa, S., Vaes, S.: Unique Cartan decomposition for II1 factors arising from arbitrary actions

of free groups. Acta Math. 212, 141–198 (2014) Zbl 1307.46047 MR 3179609

[44] Popa, S., Vaes, S.: Unique Cartan decomposition for II1 factors arising from arbitrary actions

of hyperbolic groups. J. Reine Angew. Math. 694, 215–239 (2014) Zbl 1314.46078

MR 3259044

[45] Takesaki, M.: Theory of Operator Algebras. II. Encyclopaedia Math. Sci. 125, Springer, Berlin

(2003) Zbl 1059.46031 MR 1943006

[46] Ueda, Y.: Amalgamated free product over Cartan subalgebra. Pacific J. Math. 191, 359–392

(1999) Zbl 1030.46085 MR 1738186

[47] Ueda, Y.: Factoriality, type classification and fullness for free product von Neumann algebras.

Adv. Math. 228, 2647–2671 (2011) Zbl 1252.46059 MR 2838053

[48] Ueda, Y.: Some analysis of amalgamated free products of von Neumann algebras in the nontracial setting. J. London Math. Soc. (2) 88, 25–48 (2013) Zbl 1285.46048 MR 3092256

A Self-archived copy in

Kyoto University Research Information Repository

https://repository.kulib.kyoto-u.ac.jp

Unitary conjugacy for type III subfactors and W -superrigidity

1721

[49] Ueda, Y.: A free product pair rigidity result in von Neumann algebras. J. Noncommut. Geom.

13, 587–607 (2019) Zbl 1435.46042 MR 3988756

[50] Vaes, S.: Rigidity for von Neumann algebras and their invariants. In: Proc. International

Congress of Mathematicians (Hyderabad, 2010), Vol. III, Hindustan Book Agency, New

Delhi, 1624–1650 (2010) Zbl 1235.46058 MR 2827858

[51] Vaes, S.: Normalizers inside amalgamated free product von Neumann algebras. Publ. RIMS

Kyoto Univ. 50, 695–721 (2014) Zbl 1315.46067 MR 3273307

[52] Vaes, S., Verraedt, P.: Classification of type III Bernoulli crossed products. Adv. Math. 281,

296–332 (2015) Zbl 1332.46060 MR 3366841

[53] Verraedt, P.: Bernoulli crossed products without almost periodic weights. Int. Math. Res.

Notices 2018, 3684–3720 Zbl 1437.46062 MR 3815165

[54] Voiculescu, D. V., Dykema, K. J., Nica, A.: Free Random Variables. CRM Monogr. Ser. 1,

Amer. Math. Soc., Providence, RI (1992) Zbl 0795.46049 MR 1217253

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