We investigate quantum group generalizations of various density results from Fourier analysis on compact groups. In particular, we establish the density of characters in the space of fixed points of the conjugation action on L2(G) and use this result to show the weak∗ density and norm density of characters in ZL∞ (G) and ZCGG), respectively. As a corollary, we partially answer an open question of Woronowicz. At the level of L1(G), we show that the center Z(L1(G)) is precisely the closed linear span of the quantum characters for a large class of compact quantum groups, including arbitrary compact Kac algebras. In the latter setting, we show, in addition, that Z(L1(G)) is a completely complemented Z(L1(G))-sub module of L1(G).

Additional Metadata
Keywords Compact quantum group, Irreducible character
Persistent URL dx.doi.org/10.4153/CMB-2016-101-1
Journal Canadian Mathematical Bulletin
Citation
Alaghmandan, M. (Mahmood), & Crann, J. (2017). Character density in central subalgebras of compact quantum groups. Canadian Mathematical Bulletin, 60(3), 449–461. doi:10.4153/CMB-2016-101-1