Operator approximate biprojectivity of locally compact quantum groups

Abstract

We initiate a study of operator approximate biprojectivity for quantum group algebra L1(G[double-struck]), where G[double-struck] is a locally compact quantum group. We show that if L1(G[double-struck]) is operator approximately biprojective, then G[double-struck] is compact. We prove that if G[double-struck] is a compact quantum group and is a non-Kac-type compact quantum group such that both L1(G[double-struck]) and L1 are operator approximately biprojective, then L1(G[double-struck])⊗ L1 is operator approximately biprojective, but not operator biprojective. © 2018 by the Tusi Mathematical Research Group.