Cohomology of Hopf C* -Algebras and Hopf Von Neumann Algebras
Copyright policy )Cohomology of Hopf C* -Algebras and Hopf Von Neumann Algebras
In this article, we will define two canonical cohomology theories for Hopf $C^*$-algebras and for Hopf von Neumann algebras (with coefficients in their bicomodules). We will then study the situations when these cohomologies vanish. The cases of locally compact groups and compact quantum groups will be considered in more details.
The first statement of Remark 1.9(a) in the original published article (in Proc. LMS) does not follow directly from Lemma 1.7(a) but it does follow very easily from the argument of Proposition 1.10. Therefore, we change the presentations of Remark 1.9 and Proposition 1.10 (one line is added in the proof of Proposition 1.10)
- Queen's University Belfast United Kingdom
- Queen's University Canada
46L55, 46L05 (Primary) 43A07, 22D25 (Secondary), \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations, Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, Mathematics - Quantum Algebra, Mathematics - Operator Algebras, FOS: Mathematics, Hopf von Neumann algebra, cohomology, Quantum Algebra (math.QA), Operator Algebras (math.OA), Hopf \(C^*\)-algebra
46L55, 46L05 (Primary) 43A07, 22D25 (Secondary), \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations, Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, Mathematics - Quantum Algebra, Mathematics - Operator Algebras, FOS: Mathematics, Hopf von Neumann algebra, cohomology, Quantum Algebra (math.QA), Operator Algebras (math.OA), Hopf \(C^*\)-algebra
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