Compact quantum groups generated by their tori

Abstract

Associated to any closed subgroup $G\subset U_N^{+}$ is a family of toral subgroups $T_Q\subset G$, indexed by the unitary matrices $Q\in U_N$. The family $\{T_Q|Q\in U_N\}$ is expected to encode the main properties of $G$, and there are several conjectures in this sense. We verify here the generation conjecture, $G=<T_Q|Q\in U_N>$, for various classes of compact quantum groups. Our results generalize the previously known facts on the subject.

Withdrawn by the author - the main findings in this paper are now part of arXiv:1909.08152

References in corpus (2)

• Categories of Two-Colored Pair Partitions, Part II: Categories Indexed by Semigroups
• A note on the half-liberation operation

Cited by in corpus (1)

• Hopf algebras with enough quotients