TY - JOUR

T1 - A note on nonunital absorbing extensions

AU - Gabe, James

PY - 2016/8/30

Y1 - 2016/8/30

N2 - Elliott and Kucerovsky stated that a nonunital extension of separable C*-algebras with a stable ideal is nuclearly absorbing if and only if the extension is purely large. However, their proof was flawed. We give a counterexample to their theorem as stated, but establish an equivalent formulation of nuclear absorption under a very mild additional assumption to being purely large. In particular, if the quotient algebra is nonunital, then we show that the original theorem applies. We also examine how this affects results in classification theory.

AB - Elliott and Kucerovsky stated that a nonunital extension of separable C*-algebras with a stable ideal is nuclearly absorbing if and only if the extension is purely large. However, their proof was flawed. We give a counterexample to their theorem as stated, but establish an equivalent formulation of nuclear absorption under a very mild additional assumption to being purely large. In particular, if the quotient algebra is nonunital, then we show that the original theorem applies. We also examine how this affects results in classification theory.

KW - Absorbing extensions

KW - Classification

KW - Corona factorisation property

KW - KK-theory

U2 - 10.2140/pjm.2016.284.383

DO - 10.2140/pjm.2016.284.383

M3 - Journal article

VL - 284

SP - 383

EP - 393

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -