MathDB4 problems
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UCT conjecture for separable nuclear -algebras
A separable nuclear -algebra is a -algebra whose underlying -algebra is separable and nuclear. The bootstrap category is the class of -algebras to which the Uni…
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Finite nuclear dimension implies finite complexity relative to subhomogeneous algebras
Relative complexity conjecture. Every separable -algebra with finite nuclear dimension has finite complexity relative to the class of subhomogeneous -algebras.
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Kirchberg algebras have complexity rank at most two
Kirchberg complexity-rank conjecture. Every UCT Kirchberg algebra has complexity rank at most two.
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Finite nuclear dimension and real rank zero imply finite complexity
Finite-complexity conjecture. Every separable -algebra with finite nuclear dimension and real rank zero has finite complexity.