Annals of Functional Analysis

Operator approximate biprojectivity of locally compact quantum groups

Mohammad Reza Ghanei and Mehdi Nemati

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We initiate a study of operator approximate biprojectivity for quantum group algebra L1(G), where G is a locally compact quantum group. We show that if L1(G) is operator approximately biprojective, then G is compact. We prove that if G is a compact quantum group and H is a non-Kac-type compact quantum group such that both L1(G) and L1(H) are operator approximately biprojective, then L1(G)ˆL1(H) is operator approximately biprojective, but not operator biprojective.

Article information

Ann. Funct. Anal., Volume 9, Number 4 (2018), 514-524.

Received: 17 June 2017
Accepted: 20 November 2017
First available in Project Euclid: 4 May 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L89: Other "noncommutative" mathematics based on C-algebra theory [See also 58B32, 58B34, 58J22]
Secondary: 46M10: Projective and injective objects [See also 46A22] 46L07: Operator spaces and completely bounded maps [See also 47L25]

locally compact quantum group operator approximate biprojectivity tensor product of compact quantum groups


Ghanei, Mohammad Reza; Nemati, Mehdi. Operator approximate biprojectivity of locally compact quantum groups. Ann. Funct. Anal. 9 (2018), no. 4, 514--524. doi:10.1215/20088752-2017-0065.

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