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MiS Preprint
92/2018
Associated noncommutative vector bundles over the Vaksman-Soibelman quantum complex projective spaces
Francesca Arici, Piotr M. Hajac and Mariusz Tobolski
By a diagonal embedding of $U(1)$ in $SU_q(m)$, we prolongate the diagonal circle action on the Vaksman-Soibelman quantum sphere $\bS^{2n+1}_q$ to the $SU_q(m)$-action on the prolongated bundle. Then we prove that the noncommutative vector bundles associated via the fundamental representation of $SU_q(m)$, for $m\in\{2,\ldots,n\}$, yield generators of the even K-theory group of the C*-algebra of the Vaksman--Soibelman quantum complex projective space $\mathbb{C}{\rm P}^n_q$.
