In this paper, we investigate projectivity in the category of operator spaces. In particular, we show that the Fourier algebra of a locally compact group $G$ is operator biprojective if and only if $G$ is discrete.

Keywords:

locally compact group, Fourier algebra, operator space, projective locally compact group, Fourier algebra, operator space, projective

MSC Classifications:

13D03, 18G25, 43A95, 46L07, 22D99 show english descriptions (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen, cyclic, dihedral, etc.)
Relative homological algebra, projective classes
Categorical methods [See also 46Mxx]
Operator spaces and completely bounded maps [See also 47L25]
None of the above, but in this section 13D03 - (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen, cyclic, dihedral, etc.)
18G25 - Relative homological algebra, projective classes
43A95 - Categorical methods [See also 46Mxx]
46L07 - Operator spaces and completely bounded maps [See also 47L25]
22D99 - None of the above, but in this section

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