2-cocycles and twisting of Kac algebras
The paper describes twisting of Hopf-von Neumann and Kac algebras by 2-cocycles, and can be viewed as a generalisation of [\textit{M. Enock} and \textit{L. Vainerman}, Commun. Math. Phys. 178, No. 3, 571-596 (1996; Zbl 0876.46042)]. It is shown that in the case of a Kac algebra, if the twisting 2-cocycle is lifted from a 2-cocycle on a locally compact subgroup whose image belongs to the centralizer of the Haar weight, then the coinvolutive Hopf-von Neumann algebra with undeformed Haar weight obtained by twisting is a Kac algebra. Quantisations of the Heisenberg group and several series of \(C^*\)-Hopf algebras of finite dimensions \(4n\) and \(2n^2\) obtained by twisting of finite groups are given as examples.
coinvolutive Hopf-von Neumann algebra with undeformed Haar weight
scientific article; zbMATH DE number 1213872