A maximality result for orthogonal quantum groups

Abstract

We prove that the quantum group inclusion $O_n\subset O_n^{\ast }$ is "maximal", where $O_n$ is the usual orthogonal group and $O_n^{\ast }$ is the half-liberated orthogonal quantum group, in the sense that there is no intermediate compact quantum group $O_n\subset G\subset O_n^{\ast }$. In order to prove this result, we use: (1) the isomorphism of projective versions $P{O}_n^{\ast }\simeq P{U}_n$, (2) some maximality results for classical groups, obtained by using Lie algebras and some matrix tricks, and (3) a short five lemma for cosemisimple Hopf algebras.

10 pages

References in corpus (2)

• De Finetti theorems for easy quantum groups
• Examples of inner linear Hopf algebras

Cited by in corpus (6)

• The Connes embedding property for quantum group von Neumann algebras
• Categories of Two-Colored Pair Partitions, Part II: Categories Indexed by Semigroups
• Homogeneous quantum groups and their easiness level
• The full classification of orthogonal easy quantum groups
• A Connection between Easy Quantum Groups, Varieties of Groups and Reflection Groups
• Generating linear categories of partitions