Research Projects

The goal of the project is to classify all graph C*-algebras which are S^{1}-quantum principal bundles over base spaces which are also graph C*-algebras. The motivating example is quantum sphere and quantum projective space. The crossed products with respect to the integer action on C*-algebras are particular examples of S^{1}-quantum principal bundles. The K-theory of crossed product by integer group actions are well known and are computable via Pimsmer-Voiculescu sequence. Researchers propose to develop tools to compute the K-theory of the S^{1}-quantum principal bundles and see if there is any K-theoretic obstruction to graph C*-algebras being a S^{1}-quantum principal bundles.