Character Density in Central Subalgebras of Compact Quantum Groups
Journal article, 2017

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 L-2 (G) and use this result to show the weak* density and norm density of characters in ZL(infinity) (G) and ZC (G), respectively. As a corollary, we partially answer an open question of Woronowicz. At the level of L-1(G), we show that the center Z (L-1(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 (L-1(G)) is a completely complemented Z (L-1(G))-submodule of L-1(G).

irreducible character

compact quantum group


Mahmood Alaghmandan

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Jason Crann

Carleton University

Canadian Mathematical Bulletin

0008-4395 (ISSN) 1496-4287 (eISSN)

Vol. 60 3 449-461

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