2 citations · 4 across the 9 of their papers we have counts for
9 papers
On Braided Differential Calculi and Quantum G-structures
Antonio Del Donno, Giovanni Gava, Emanuele Latini +1
We develop a theory of first order differential calculi in braided monoidal categories and classify braided covariant and bicovariant calculi on braided Hopf algebras. We show that…
An infinitesimal deformation of the post-Lie and post-Hopf algebra correspondence
Andrea Rivezzi, Andrea Sciandra, Thomas Weber
We describe infinitesimal deformations of post-Lie algebras and post-Hopf algebras and prove that the adjunction given by the universal enveloping algebra and primitive elements fu…
Noncommutative vector field calculi
Rita Fioresi, Emanuele Latini, Thomas Weber
We discuss noncommutative differential geometry from a vector field centric point of view. This is based on the notion of first order vector field calculus (FOVC), which has been p…
Takeuchi-Schneider equivalence and calculi for homogeneous spaces of Hopf algebroids
Niels Kowalzig, Thomas Weber
We develop a notion of covariant differential calculus for Hopf algebroids. As a byproduct, we prove analogues of the fundamental theorem of Hopf modules and a Takeuchi-Schneider e…
Gauge transformations on quantum principal bundles
Antonio Del Donno, Emanuele Latini, Thomas Weber
We understand quantum principal bundle as faithfully flat Hopf--Galois extensions, with a structure Hopf algebra coacting on a total space algebra and with base algebra given by th…
Quantization of infinitesimal braidings and pre-Cartier quasi-bialgebras
Chiara Esposito, Andrea Rivezzi, Jonas Schnitzer +1
In this paper we extend Cartier's deformation theorem of braided monoidal categories admitting an infinitesimal braiding to the non-symmetric case. The algebraic counterpart of the…
On the Durdevic approach to quantum principal bundles
Antonio Del Donno, Emanuele Latini, Thomas Weber
We revisit and extend the Durdevic theory of complete calculi on quantum principal bundles. In this setting one naturally obtains a graded Hopf-Galois extension of the higher order…
The Geometry of Quantum Computing
E. Ercolessi, R. Fioresi, T. Weber
In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we…
Infinitesimal braidings and pre-Cartier bialgebras
A. Ardizzoni, L. Bottegoni, A. Sciandra +1
We propose an infinitesimal counterpart to the notion of braided category. The corresponding infinitesimal braidings are natural transformations which are compatible with an underl…