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Character Density in Central Subalgebras of Compact Quantum Groups

Mahmood Alaghmandan (Institutionen för matematiska vetenskaper, Analys och sannolikhetsteori) ; J. Crann
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques (0008-4395). Vol. 60 (2017), 3, p. 449-461.
[Artikel, refereegranskad vetenskaplig]

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).

Nyckelord: compact quantum group, irreducible character



Denna post skapades 2017-09-05.
CPL Pubid: 251624

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, Analys och sannolikhetsteoriInstitutionen för matematiska vetenskaper, Analys och sannolikhetsteori (GU)

Ämnesområden

Matematik

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