19 citations · 37 across the 18 of their papers we have counts for
19 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…
Levi-Civita connection on the irreducible quantum flag manifolds
Jyotishman Bhowmick, Bappa Ghosh, Andrey O. Krutov +1
We classify covariant metrics (in the sense of Beggs and Majid) on a class of quantum homogeneous spaces. In particular, our classification implies the existence of a unique (up to…
Lusztig's Quantum Root Vectors and a Dolbeault Complex for the A-Series Full Quantum Flag Manifolds
Réamonn Ó Buachalla, Petr Somberg
For the Drinfeld-Jimbo quantum enveloping algebra , we show that the span of Lusztig's positive root vectors, with respect to Littlemann's nice reduced decomp…
Curvature of positive relative line modules over the quantum projective spaces
Andrey O. Krutov, Réamonn Ó Buachalla
We show that the curvature of a positive relative line module over quantum projective space is given by -integer deformation of its classical curvature. This generalises a resul…
A remark on the Hochschild dimension of liberated quantum groups
Tomasz Brzeziński, Ulrich Krähmer, Réamonn Ó Buachalla +1
Let be a Hopf algebra equipped with a projection onto the coordinate Hopf algebra of a semisimple algebraic group . It is shown that if admits a suitabl…
Spectral gaps for twisted Dolbeault-Dirac operators over the irreducible quantum flag manifolds
Biswarup Das, Réamonn Ó Buachalla, Petr Somberg
We show that tensoring the Laplace and Dolbeault-Dirac operators of a Kähler structure (with closed integral) by a negative Hermitian holomorphic module, produces operators with sp…
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…
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…
Positive Line Bundles Over the Irreducible Quantum Flag Manifolds
Fredy Díaz García, Andrey Krutov, Réamonn Ó Buachalla +2
Noncommutative Kähler structures were recently introduced by the second author as a framework for studying noncommutative Kähler geometry on quantum homogeneous spaces. It was subs…
A Dolbeault-Dirac Spectral Triple for Quantum Projective Space
Biswarup Das, Réamonn Ó Buachalla, Petr Somberg
The notion of a Kähler structure for a differential calculus was recently introduced by the second author as a framework in which to study the noncommutative geometry of the quantu…
A Kodaira Vanishing Theorem for Noncommutative Kahler Structures
Réamonn Ó Buachalla, Jan Stovicek, Adam-Christiaan van Roosmalen
Using the framework of noncommutative Kahler structures, we generalise to the noncommutative setting the celebrated vanishing theorem of Kodaira for positive line bundles. The resu…
Nichols Algebras and Quantum Principal Bundles
Andrey Krutov, Réamonn Ó Buachalla, Karen R. Strung
We introduce a general framework for associating to a homogeneous quantum principal bundle a Yetter-Drinfeld module structure on the cotangent space of the base calculus. The holom…
A Borel-Weil Theorem for the Quantum Grassmannians
Alessandro Carotenuto, Colin Mrozinski, Réamonn Ó Buachalla
We establish a noncommutative generalisation of the Borel-Weil theorem for the Heckenberger-Kolb calculi of the quantum Grassmannians. The result is formulated in the framework of…
Noncommutative Kähler Structures on Quantum Homogeneous Spaces
Réamonn Ó Buachalla
Building on the theory of noncommutative complex structures, the notion of a noncommutative Kähler structure is introduced. In the quantum homogeneous space case many of the fundam…
Noncommutative Kahler Geometry of the Standard Podles Sphere
Réamonn Ó Buachalla
Building on the now established presentation of the standard Podles sphere as an example of a noncommutative complex structure, we investigate how its classical Kahler geometry beh…
Noncommutative Complex Structures on Quantum Homogeneous Spaces
Réamonn Ó Buachalla
A new framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categor…
MSc Thesis: Presentation of Certain New Trends in Noncommutative Geometry
Réamonn Ó Buachalla
MSc thesis of the author offering an introduction to the operator algebraic approach to noncommutative geometry, with a treatment of some more advanced elements such as the noncomm…
Quantum Bundle Description of the Quantum Projective Spaces
Réamonn Ó Buachalla
We realise Heckenberger and Kolb's canonical calculus on quantum projective (n-1)-space as the restriction of a distinguished quotient of the standard bicovariant calculus for Cq[S…