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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

Abstract

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 $\mathbb{C}{\rm P}^n_q$.

Received:
29.10.18
Published:
30.10.18
MSC Codes:
46L80, 46L85, 58B32
Keywords:
K-theory, noncommutative vector bundle, compact quantum group, Peter–Weyl decomposition, principal comodule algebra

Related publications

Preprint
2018 Repository Open Access
Francesca Arici, Piotr M. Hajac and Mariusz Tobolski

Associated noncommutative vector bundles over the Vaksman-Soibelman quantum complex projective spaces