Theoretical Statistics and Mathematics Unit, ISI Delhi

Remark on Poincar\'e duality for $SU_q(2)$

by Partha Sarathi Chakraborty and Arupkumar Pal

Let $\mathcal{A}$ be the $C^{\ast}$-algebra associated with $SU_q (2)$, $J$ be the modular conjugation coming
from the Haar state and let $D$ be the generic equivariant Dirac operator for $SU_q (2)$. We
prove in this article that there is no element in $J\mathcal{A}J$, other than the scalars, that have
bounded commutator with $D$. This shows in particular that $J\mathcal{A}J$ does not contain any
Poincar\'{e} dual for $SU_q (2)$.

isid/ms/2002/30 [fulltext]

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