Centrally Large Subalgebras and Tracial Z-Absorption

2016/08/20 by Dawn Archey, Archey, Dawn, Julian Buck +3
Mathematics · #46L #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L

paper · pdf · doi:10.48550/arxiv.1608.05847

15 pages

arxiv created 2016/08/20 · arxiv updated 2016/08/23

Abstract

Let A be a simple infinite dimensional stably finite unital C*-algebra, and let B be a centrally large subalgebra of A. We prove that if A is tracially Z-absorbing if and only if B is tracially Z-absorbing. If A and B are also separable and nuclear, we prove that A is Z-absorbing if and only if B is Z-absorbing.

Related

• Generalized Tracially Approximated C*-algebras
• Some properties for certain generalized tracial approximated \rm C^*-algebras
• Tracially Z-absorbing C*-algebras
• Simple tracially Z-absorbing C*-algebras
• Non-unital tracially approximated \rm C^*-algebras