Nuclear dimension of simple $$\mathrm {C}^*$$-algebras
Jorge Castillejos, Samuel Evington, Aaron Tikuisis, Stuart White, Wilhelm Winter
Abstract
Abstract We compute the nuclear dimension of separable, simple, unital, nuclear, $${\mathcal {Z}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Z</mml:mi></mml:math> -stable $$\mathrm {C}^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mo>∗</mml:mo></mml:msup></mml:math> -algebras. This makes classification accessible from $${\mathcal {Z}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Z</mml:mi></mml:math> -stability and in particular brings large classes of $$\mathrm {C}^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mo>∗</mml:mo></mml:msup></mml:math> -algebras associated to free and minimal actions of amenable groups on finite dimensional spaces within the scope of the Elliott classification programme.