Character Density in Central Subalgebras of Compact Quantum Groups

Author:

Alaghmandan Mahmood,Crann Jason

Abstract

AbstractWe 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 normdensity of characters in ZL(G) and ZC(G), 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))-submodule of L1(G).

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Examples of compact quantum groups with L(G) a factor;Journal of Functional Analysis;2024-03

2. On the von Neumann algebra of class functions on a compact quantum group;Journal of Functional Analysis;2022-09

3. A new duality via the Haagerup tensor product;Journal of Mathematical Analysis and Applications;2019-04

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