The Kirchberg–Rørdam character criterion and infinite tensor-power Jiang–Su stability
OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
A nonzero unital separable complex C^(∗)-algebra is Jiang–Su stable exactly when its norm central-sequence algebra has no characters, for every free ultrafilter. This answers the Kirchberg–Rørdam character question. Also, the infinite minimal tensor power of every such algebra without characters is Jiang–Su stable, answering the Dadarlat–Toms question.
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MANUSCRIPT 01
The Kirchberg–Rørdam character criterion
We prove the Kirchberg–Rørdam character criterion: for every free ultrafilter on ℕ, a nonzero unital separable complex C^(∗)-algebra absorbs the Jiang–Su algebra if and only if its norm central-sequence algebra has no characters. We also prove that the infinite minimal tensor power of every nonzero unital separable complex…
Full source abstract
We prove the Kirchberg–Rørdam character criterion: for every free ultrafilter on ℕ, a nonzero unital separable complex C^(∗)-algebra absorbs the Jiang–Su algebra if and only if its norm central-sequence algebra has no characters. We also prove that the infinite minimal tensor power of every nonzero unital separable complex C^(∗)-algebra without characters is \mathcal Z-stable and contains a unital copy of \mathcal Z.
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