Compact Quantum Group Extensions of $US{p}_q(2n)$, $O_q(n)$ and $S{O}_q(2n)$

Abstract

I introduce compact quantum group extensions associated with the $q$-deformations of the classical compact groups $USp(2n)$, $O(n,\mathbb{R})$ and $SO(2n,\mathbb{R})$. Motivated by the relationship between $S{U}_q(n)$ and $U_q(n)$, I study the problem of constructing compact quantum groups $Z_{q,n}$ extending the standard compact quantum groups $A_{q,n}\in \{US{p}_q(2n),O_q(N),S{O}_q(2n)\}$ through an additional central unitary element.