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 -