507 citations · 2.1k across the 59 of their papers we have counts for
63 papers
Bianchi identities in noncommutative geometry
Paolo Aschieri
We first present an introduction to the differential geometry of noncommutative algebras that carry a representation of a triangular Hopf algebra. Their noncommutativity is encoded…
Atiyah sequences of braided Lie algebras and their splittings
Paolo Aschieri, Giovanni Landi, Chiara Pagani
Associated with an equivariant noncommutative principal bundle we give an Atiyah sequence of braided derivations whose splittings give connections on the bundle. Vertical braided d…
Braided Hopf algebras and gauge transformations II: -structures and examples
Paolo Aschieri, Giovanni Landi, Chiara Pagani
We consider noncommutative principal bundles which are equivariant under a triangular Hopf algebra. We present explicit examples of infinite dimensional braided Lie and Hopf algebr…
Noncommutative gauge and gravity theories and geometric Seiberg-Witten map
Paolo Aschieri, Leonardo Castellani
We give a pedagogical account of noncommutative gauge and gravity theories, where the exterior product between forms is deformed into a -product via an abelian twist (e.g. t…
Metric compatibility and Levi-Civita Connections on Quantum Groups
Paolo Aschieri, Thomas Weber
Arbitrary connections on a generic Hopf algebra are studied and shown to extend to connections on tensor fields. On this ground a general definition of metric compatible connec…
Braided Hopf algebras and gauge transformations
Paolo Aschieri, Giovanni Landi, Chiara Pagani
We study infinitesimal gauge transformations of an equivariant noncommutative principal bundle as a braided Lie algebra of derivations. For this, we analyse general -braided Hop…