11 citations · 23 across the 8 of their papers we have counts for
8 papers
Covariant Bimodule Connections and Noncommutative Geometric Yang-Baxter Solutions
Alessandro Carotenuto, Antonio Del Donno, Antonio Del Dono +2
We introduce a new class of Yang--Baxter solutions, which we call \emph{noncommutative geometric solutions}, constructed from quantum group noncommutative geometries. These solutio…
Noncommutative Complex Structures for the Full Quantum Flag Manifold of Quantum SU(3)
Alessandro Carotenuto, Réamonn Ó Buachalla, Junaid Razzaq
In recent work, Lusztig's positive root vectors (with respect to a distinguished choice of reduced decomposition of the longest element of the Weyl group) were shown to give a quan…
Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds
Alessandro Carotenuto, Réamonn Ó Buachalla
It was recently shown (by the second author and Díaz García, Krutov, Somberg, and Strung) that every relative line module over an irreducible quantum flag manifold $\mathcal{O}_q(G…
Principal Pairs of Quantum Homogeneous Spaces
Alessandro Carotenuto, Réamonn Ó Buachalla
We propose a simple but effective framework for producing examples of covariant faithfully flat (generalised) Hopf-Galois extensions from a nested pair of quantum homogeneous space…
A Borel-Weil theorem for the irreducible quantum flag manifolds
Alessandro Carotenuto, Fredy Díaz García, Réamonn Ó Buachalla
We establish a noncommutative generalisation of the Borel-Weil theorem for the Heckenberger-Kolb calculi of the irreducible quantum flag manifolds , generalis…
The Weyl-Mellin quantization map for -Minkowski Noncommutative Spacetime
Alessandro Carotenuto, Fedele Lizzi, Mattia Manfredonia +1
We present a quantization of the functions of spacetime, i.e.\ a map, analog to Weyl map, which reproduces the -Minkowski commutation relations, and it has the desirable propert…
Spin geometry of the rational noncommutative torus
Alessandro Carotenuto, Ludwik Dabrowski
The twined almost commutative structure of the standard spectral triple on the noncommutative torus with rational parameter is exhibited, by showing isomorphisms with a spectral tr…
Differential calculus on Jordan algebra and Jordan modules
Alessandro Carotenuto, Ludwik Dabrowski, Michel Dubois-Violette
Having in mind applications to particle physics we develop the differential calculus over Jordan algebras and the theory of connections on Jordan modules. In particular we focus on…