We review the present status of gauge theories built on various quantum space–times
described by noncommutative space–times. The mathematical tools and notions underlying …

We provide a differential structure on arbitrary cleft extensions B:= A co H⊆ A for an H-
comodule algebra A. This is achieved by constructing a covariant calculus on the …

In this paper we develop the theory of reduction of quantum principal bundles over
projective bases. We show how the sheaf theoretic approach can be effectively applied to …

Hopf Algebras, Quantum Groups and Yang-Baxter Equations Page 1 axioms Hopf Algebras,
Quantum Groups and Yang-Baxter Equations Florin Felix Nichita www. mdpi. com/journal/axioms …

We study spectral triples over noncommutative principal U (1)-bundles of arbitrary
dimension and a compatibility condition between the connection and the Dirac operator on …

We review Hopf-Galois extensions, in particular faithfully flat ones, accepted to be the
noncommutative algebraic dual of a principal bundle. We also make a short digression into …

Representing Z= NZ as roots of unity, we restrict a natural U. 1/-action on the Heegaard
quantum sphere to Z= NZ, and call the quotient spaces Heegaard quantum lens spaces …

In this thesis I discuss some results on the noncommutative (spin) geometry of quantum
principal G-bundles. The first part of the thesis is devoted to the study of spectral triples over …

Recent results by Krähmer [Israel J. Math. 189 (2012), 237-266] on smoothness of Hopf-
Galois extensions and by Liu [arXiv: 1304.7117] on smoothness of generalized Weyl …

The algebraic approach to bundles in non-commutative geometry and the definition of
quantum real weighted projective spaces are reviewed. Principal U (1)-bundles over …