Abstract:
Abstract: In this thesis, we study quantum symmetries within the realm
of noncommutative geometry. These symmetries are captured in two
levels of generality, namely, Hopf algebras (or compact quantum
groups) in the context of noncommutative differential geometry a la
Connes and Hopf algebroids in the context of noncommutative Kaehler
geometry a la Ó Buachalla. We compute the orientation-preserving
quantum isometry group of the Chakraborty-Pal spectral triple on the
odd sphere. Generalizing the Hopf algebra case, we build a framework
to take into account Hopf algebroid equivariance in non-commutative complex geometry. We classify complex structures on a canonical spectral triple over the three-point space and identify a universal Hopf algebroid acting on a finite space.
