Permanence of stable rank one for centrally large subalgebras and crossed products by minimal homeomorphisms
Dawn Archey, N. Christopher Phillips
Abstract
We prove that if A is an infinite dimensional simple separable unital C∗-algebra which contains a centrally large subalgebra with stable rank one, then A has stable rank one. We use this result to prove that the Giol--Kerr examples of minimal homeomorphisms give crossed products with stable rank one but which are not stable under tensoring with the Jiang--Su algebra and are therefore not classifiable in terms of the Elliott invariant.
Topics & Concepts
MathematicsSeparable spaceSubalgebraRank (graph theory)UnitalInvariant (physics)Simple (philosophy)Pure mathematicsCrossed productAlgebra over a fieldCombinatoricsMathematical analysisEpistemologyMathematical physicsPhilosophyAdvanced Operator Algebra ResearchAdvanced Topics in AlgebraAlgebraic structures and combinatorial models