• 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 ...
    • 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 ...