Biprojective algebras and operator spaces
type: Item
instance of: scholarly article
title: Biprojective algebras and operator spaces
zbMATH Open document ID: 1011.46045
DOI: 10.1023/A:1016047626689
published in: Journal of Mathematical Sciences (New York)
publication date: 2003-06-11T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 46H25
Mathematics Subject Classification ID: 46M20
Mathematics Subject Classification ID: 46M18
zbMATH DE Number: 1821731
zbMATH Keywords: projective Banach bimodule
zbMATH Keywords: quantized functional analysis
zbMATH Keywords: biprojective operator algebras
zbMATH Keywords: biprojective quantized algebras
zbMATH Keywords: cohomology groups
author: Oleg Yu. Aristov
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
full work available at URL: a:1016047626689
OpenAlex ID: W79236015
description: scientific article; zbMATH DE number 1821731