Biprojective algebras and operator spaces (Q1848059)

A Banach algebra is called biprojective if it is a projective Banach bimodule over itself. The structure of semisimple biprojective Banach algebras with the approximation property was described by \textit{Yu. V. Selivanov} in his fundamental paper [Math. USSR, Izv. 15, 387-399 (1980); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 43, 1159-1174 (1979; Zbl 0434.46050)]. The present work extends the biprojectivity in the quantized functional analysis context, introducing biprojective operator algebras and biprojective quantized algebras. For such algebras the author proves structure theorems and finds their cohomology groups [see also \textit{Yu. V. Selivanov}, Monatsh. Math. 128, 35-60 (1999; Zbl 0951.46042)].