Quasidiagonality of extensions of quasidiagonal CC^*-algebras

Let II, AA, and BB be CC^*-algebras in a short exact sequence

0IιAπB0.0\longrightarrow I\xrightarrow{\iota}A\xrightarrow{\pi}B\longrightarrow 0.

Assume that II and BB are separable, nuclear, and quasidiagonal. Extension quasidiagonality conjecture. Then AA is quasidiagonal if and only if AA is stably finite. The question is a restricted form of the Blackadar–Kirchberg conjecture, motivated by the fact that extensions of quasidiagonal algebras need not be quasidiagonal without a stable finiteness condition. Its status is not resolved by the supplied source information.

Sources & referencesView supporting material

Primary source

Iason Moutzouris, “Extensions of quasidiagonal C^*-algebras and controlling the K_0-map of embeddings”, arXiv:2112.03224 (2022).

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