clopen.solutions

Open problems

980 registered problems.

OP-00960 Open
Indices of irreducible subfactors of the hyperfinite II₁ factor
OA · hyperfinite II₁ factor · Jones index · Peterson's operator algebra problems · subfactors
OP-00961 Open
Does every nonamenable II₁ factor contain the free group factor L(F₂)?
OA · amenability · free group factors · II₁ factors · Peterson's operator algebra problems
OP-00962 Open
The Stone–Weierstrass problem for C*-algebras
OA · C*-algebras · Peterson's operator algebra problems · pure states · Stone–Weierstrass theorem
OP-00963 Open
Are the radial and generator masas of L(F₂) conjugate by an automorphism?
OA · free group factors · maximal abelian subalgebras · Peterson's operator algebra problems · radial masa
OP-00964 Open
Do reduced group C*-algebras remember torsion-free groups?
OA · C*-superrigidity · Peterson's operator algebra problems · reduced group C*-algebras · torsion-free groups
OP-00965 Open
Tensor factors of McDuff II₁ factors
OA · central sequences · McDuff factors · Peterson's operator algebra problems · tensor products
OP-00966 Open
Uniqueness of McDuff decompositions up to amplification
OA · amplifications · McDuff decomposition · McDuff factors · Peterson's operator algebra problems
OP-00967 Open
Tensor products of maximal injective subalgebras
OA · II₁ factors · maximal injective subalgebras · Peterson's operator algebra problems · tensor products
OP-00968 Open
Kadison's problem on finitely generated *-algebras of operators with finite spectra
OA · *-algebras · finite spectrum · operator algebras · Peterson's operator algebra problems
OP-00969 Open
Cocycle superrigidity of Bernoulli actions of groups with vanishing first ℓ²-Betti number
OA · Bernoulli actions · cocycle superrigidity · ℓ²-Betti numbers · Peterson's operator algebra problems
OP-00970 Open
Trivial fundamental group for Bernoulli crossed products
OA · Bernoulli actions · fundamental group of II₁ factors · ℓ²-Betti numbers · Peterson's operator algebra problems
OP-00971 Open
Popa's factorial commutant embedding problem
OA · hyperfinite II₁ factor · Peterson's operator algebra problems · relative commutants · ultrapowers
OP-00972 Open
Isomorphism of matrix ultraproducts under the continuum hypothesis
OA · continuous model theory · continuum hypothesis · matrix algebras · Peterson's operator algebra problems · ultraproducts
OP-00973 Open
Cost of a group and its first ℓ²-Betti number
GR · cost · ℓ²-Betti numbers · measured group theory · Peterson's operator algebra problems
OP-00974 Open
Nonamenable subfactors of the free group factor L(F₂)
OA · free group factors · interpolated free group factors · Peterson's operator algebra problems · subfactors
OP-00975 Open
A discrete copy of the free group in the unitary group of the hyperfinite II₁ factor
OA · discrete subgroups · free groups · hyperfinite II₁ factor · Peterson's operator algebra problems · unitary groups
OP-00976 Open
Unitary representations of higher-rank lattices in the hyperfinite II₁ factor
OA · hyperfinite II₁ factor · lattices in Lie groups · Peterson's operator algebra problems · rigidity · unitary representations
OP-00977 Open
Unique Cartan subalgebra for Bernoulli crossed products
OA · Bernoulli actions · Cartan subalgebras · group measure space construction · Peterson's operator algebra problems
OP-00978 Open
Unique Cartan subalgebra for SLₙ(ℤ) acting on the n-torus
OA · Cartan subalgebras · group measure space construction · Peterson's operator algebra problems · toral automorphisms
OP-00979 Open
Unique Cartan subalgebras for groups with a nonzero ℓ²-Betti number
OA · Cartan subalgebras · C-rigidity · ℓ²-Betti numbers · Peterson's operator algebra problems
OP-00980 Open
Are locally reflexive C*-algebras exact?
OA · C*-algebras · exactness · local reflexivity · Peterson's operator algebra problems