92 citations · 277 across the 24 of their papers we have counts for
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The Einstein condition for quantum irreducible flag manifolds
Marco Matassa
We show that any quantum irreducible flag manifold satisfies an analogue of the Einstein condition, expressing proportionality between the Ricci tensor and the metric, at least in…
Equivariant quantizations of the positive nilradical and covariant differential calculi
Marco Matassa
Consider a decomposition of the positive nilradical of a complex semisimple Lie algebra of rank , where each…
Crystal limits of compact semisimple quantum groups as higher-rank graph algebras
Marco Matassa, Robert Yuncken
Let denote the quantized coordinate ring over the field of rational functions corresponding to a compact semisimple Lie group , equipped with its *-stru…
Quantum Riemannian geometry of quantum projective spaces
Marco Matassa
We study the quantum Riemannian geometry of quantum projective spaces of any dimension. In particular we compute the Riemann and Ricci tensors, using previously introduced quantum…
Fubini-Study metrics and Levi-Civita connections on quantum projective spaces
Marco Matassa
We introduce analogues of the Fubini-Study metrics and the corresponding Levi-Civita connections on quantum projective spaces. We define the quantum metrics as two-tensors, symmetr…
Twisted Hochschild Homology of Quantum Flag Manifolds and Kähler Forms
Marco Matassa
We study the twisted Hochschild homology of quantum flag manifolds, the twist being the modular automorphism of the Haar state. We prove that every quantum flag manifold admits a n…
Kähler structures on quantum irreducible flag manifolds
Marco Matassa
We prove that all quantum irreducible flag manifolds admit Kähler structures, as defined by Ó Buachalla. In order to show this result, we also prove that the differential calculi d…
The Parthasarathy formula and a spectral triple for the quantum Lagrangian Grassmannian of rank two
Marco Matassa
We show that the Dolbeault--Dirac operator on the quantum Lagrangian Grassmannian of rank two, an example of a quantum irreducible flag manifold, satisfies an appropriate version o…
Quantum flag manifolds, quantum symmetric spaces and their associated universal K-matrices
Kenny De Commer, Marco Matassa
Let be a connected, simply connected compact Lie group with complexification . Let and be the associated Lie algebras. Let be the Dynkin di…
On PBW-deformations of braided exterior algebras
Marco Matassa
We classify PBW-deformations of quadratic-constant type of certain quantizations of exterior algebras. These correspond to the fundamental modules of quantum , the…
Twisted Hochschild homology of quantum flag manifolds: 2-cycles from invariant projections
Marco Matassa
We study the twisted Hochschild homology of quantum full flag manifolds, with the twist being the modular automorphism of the Haar state. We show that non-trivial 2-cycles can be c…
Dolbeault-Dirac operators, quantum Clifford algebras and the Parthasarathy formula
Marco Matassa
We consider Dolbeault-Dirac operators on quantized irreducible flag manifolds as defined by Krähmer and Tucker-Simmons. We show that, in general, these operators do not satisfy a f…
Commutation relations for quantum root vectors of cominuscole parabolics
Marco Matassa
We prove a result for the commutator of quantum root vectors corresponding to cominuscole parabolics. Specifically we show that, given two quantum root vectors, belonging respectiv…
On the Dolbeault-Dirac operators on quantum projective spaces
Marco Matassa
We consider Dolbeault-Dirac operators on quantum projective spaces, following Krahmer and Tucker-Simmons. The main result is an explicit formula for their squares, up to terms in t…
An analogue of Weyl's law for quantized irreducible generalized flag manifolds
Marco Matassa
We prove an analogue of Weyl's law for quantized irreducible generalized flag manifolds. By this we mean defining a zeta function, similarly to the classical setting, and showing t…
Quantum Dimension and Quantum Projective Spaces
Marco Matassa
We show that the family of spectral triples for quantum projective spaces introduced by D'Andrea and Dabrowski, which have spectral dimension equal to zero, can be reconsidered as…