A simple separable unital nuclear C*-algebra without uniform property Γ is constructed, answering a 2025 open question via Thom-Porteous/Schubert calculus.
Nonstable K-theory for Z-stable C*-algebras
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abstract
Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state. Let A != 0 be a unital C^*-algebra with A = A tensor Z. Then the homotopy groups of the group U(A) of unitaries in A are stable invariants, namely, \pi_i(U(A)) = K_{i-1}(A) for all integers i >= 0. Furthermore, A has cancellation for full projections, and satisfies the comparability question for full projections. Analogous results hold for non-unital Z-stable C^*-algebras.
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Equivariant homotopy groups of automorphism groups for Kirchberg algebras under compact group actions are expressed using equivariant KK-theory, extending Dadarlat's result, alongside a unified equivariant Dadarlat-Pennig theory.
A compilation of 99 open problems in the structure and classification of nuclear C*-algebras.
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Schubert Calculus and uniform property $\Gamma$
A simple separable unital nuclear C*-algebra without uniform property Γ is constructed, answering a 2025 open question via Thom-Porteous/Schubert calculus.
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The homotopy groups of the equivariant automorphism group of Kirchberg algebras with compact group actions and equivariant Dadarlat-Pennig theory
Equivariant homotopy groups of automorphism groups for Kirchberg algebras under compact group actions are expressed using equivariant KK-theory, extending Dadarlat's result, alongside a unified equivariant Dadarlat-Pennig theory.
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Nuclear C*-algebras: 99 problems
A compilation of 99 open problems in the structure and classification of nuclear C*-algebras.