Second cohomology groups of the Hopf${}^{\ast }$-algebras associated to universal unitary quantum groups

Abstract

We compute the second (and the first) cohomology groups of ${}^{\ast }$-algebras associated to the universal quantum unitary groups of not neccesarily Kac type, extending our earlier results for the free unitary group $U_d^{+}$. The extended setup forces us to use infinite-dimensional representations to construct the cocycles.

23 pages; v2 corrects a few minor points. The paper will appear in the Annales de l'Institut Fourier

References in corpus (2)

• Cohomological dimensions of universal cosovereign Hopf algebras
• The RFD and KAC quotients of the Hopf*-algebras of universal orthogonal quantum groups

Cited by in corpus (1)

• Free resolutions for free unitary quantum groups and universal cosovereign Hopf algebras