Compact Quantum Group Extensions of $USp_q(2n)$, $O_q(n)$ and $SO_q(2n)$

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 $SU_q(n)$ and $U_q(n)$, I study the problem of constructing compact quantum groups $Z_{q,n}$ extending the standard compact quantum groups $A_{q,n}\in\{ {USp_q(2n), O_q(N), SO_q(2n)}\}$ through an additional central unitary element.