Browsing ODA Open Digital Archive by Author "Matassa, Marco"
Now showing items 1-10 of 10
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Crystal limits of compact semisimple quantum groups as higher-rank graph algebras
Matassa, Marco; Yuncken, Robert (Journal für die Reine und Angewandte Mathematik;, Peer reviewed; Journal article, 2023)Let Oq [K] denote the quantized coordinate ring over the field C(q) of rational functions corresponding to a compact semisimple Lie group K, equipped with its ∗-structure. Let A0 ⊂ C(q) denote the subring of regular functions ... -
Fubini-Study metrics and Levi-Civita connections on quantum projective spaces
Matassa, Marco (Peer reviewed; Journal article, 2021)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, symmetric in the appropriate sense, in terms of ... -
Kahler structures on quantum irreducible flag manifolds
Matassa, Marco (Journal of Geometry and Physics;Volume 145, November 2019, 103477, Journal article; Peer reviewed, 2019-07-11)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 defined by Heckenberger and Kolb are ... -
On PBW-Deformations of Braided Exterior Algebras
Matassa, Marco (Advances in Applied Clifford Algebras;29:8, Journal article; Journal article; Peer reviewed, 2018-11-26)We classify PBW-deformations of quadratic-constant type of certain quantizations of exterior algebras. These correspond to the fundamental modules of quantum slN, their duals, and their direct sums. We show that the first ... -
The Parthasarathy formula and a spectral triple for the quantum Lagrangian Grassmannian of rank two
Matassa, Marco (Letters in Mathematical Physics;August 2019, Volume 109, Issue 8, Journal article; Peer reviewed, 2019-02-05)Background and objective: The long-term psychosocial outcome of young adults after paediatric liver transplantation (LT) was investigated with the focus on day-to-day living. We aimed to capture patients’ subjective ... -
Quantum flag manifolds, quantum symmetric spaces and their associated universal K-matrices
De Commer, Kenny; Matassa, Marco (Advances in Mathematics;Volume 366, 3 June 2020, 107029, Journal article; Peer reviewed, 2020-06-03)Let U be a connected, simply connected compact Lie group with complexification G. Let u and g be the associated Lie algebras. Let Γ be the Dynkin diagram of g with underlying set I, and let Uq(u) be the associated quantized ... -
Quantum Riemannian geometry of quantum projective spaces
Matassa, Marco (Journal of Geometry and Physics;Volume 179, September 2022, 104611, Peer reviewed; Journal article, 2022-07-11)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 metrics and quantum Levi-Civita connections. ... -
Regularity of twisted spectral triples and pseudodifferential calculi
Matassa, Marco; Yuncken, Robert (Journal of Noncommutative Geometry;, Journal article; Peer reviewed, 2019-03-13)We investigate the regularity condition for twisted spectral triples. This condition is equivalent to the existence of an appropriate pseudodifferential calculus compatible with the spectral triple. A natural approach to ... -
Twisted hochschild homology of quantum flag manifolds and kähler forms
Matassa, Marco (SIGMA. Symmetry, Integrability and Geometry; 16 (2020), 098, Journal article; Peer reviewed, 2020-10-03)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 non-trivial class in degree two, with an ... -
Twisted Hochschild Homology of Quantum Flag Manifolds: 2-Cycles from Invariant Projections
Matassa, Marco (Journal of Algebra and Its Applications;, Journal article; Peer reviewed, 2019-12-03)We study the twisted Hochschild homology of quantum full ag manifolds, with the twist being the modular automorphism of the Haar state. We show that non-trivial 2cycles can be constructed from appropriate invariant ...