3 papers
math.QA2026
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…
math.QA2025
Cartan structure equations and Levi-Civita connection in noncommutative geometry
Paolo Aschieri
We study the differential and Riemannian geometry of algebras endowed with an action of a triangular Hopf algebra and noncommutativity compatible with the associated braidi…
math.QA2024
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…