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pro vyhledávání: '"Matassa, Marco"'
Autor:
Matassa, Marco
Consider a decomposition $\mathfrak{n} = \mathfrak{n}_1 \oplus \cdots \oplus \mathfrak{n}_r$ of the positive nilradical of a complex semisimple Lie algebra of rank $r$, where each $\mathfrak{n}_k$ is a module under an appropriate Levi factor. We show
Externí odkaz:
http://arxiv.org/abs/2404.18544
Autor:
Matassa, Marco, Yuncken, Robert
Publikováno v:
Journal f\"ur die reine und angewandte Mathematik (Crelles Journal), Volume 2023 Issue 802
Let $O_q[K]$ denote the quantized coordinate ring over the field $\mathbb{C}(q)$ of rational functions corresponding to a compact semisimple Lie group $K$, equipped with its *-structure. Let $A_0$ in $\mathbb{C}(q)$ denote the subring of regular func
Externí odkaz:
http://arxiv.org/abs/2208.13201
Autor:
Matassa, Marco
Publikováno v:
Journal of Geometry and Physics, 179 (2022): 104611
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. We show that the Riemann
Externí odkaz:
http://arxiv.org/abs/2103.06083
Autor:
Matassa, Marco
Publikováno v:
Advances in Mathematics, 393 (2021): 108101
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 the differential calculi intr
Externí odkaz:
http://arxiv.org/abs/2010.03291
Autor:
Matassa, Marco
Publikováno v:
SIGMA 16 (2020), 098, 18 pages
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 explicit representative define
Externí odkaz:
http://arxiv.org/abs/2003.10305
Autor:
Matassa, Marco
Publikováno v:
Journal of Geometry and Physics Volume 145 (2019), 103477
We prove that all quantum irreducible flag manifolds admit K\"ahler structures, as defined by \'O Buachalla. In order to show this result, we also prove that the differential calculi defined by Heckenberger and Kolb are differential *-calculi in a na
Externí odkaz:
http://arxiv.org/abs/1901.09544
Autor:
Matassa, Marco
Publikováno v:
Lett Math Phys (2019)
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 of the Parthasarathy formula. We use this result to complete the proof
Externí odkaz:
http://arxiv.org/abs/1810.06456
Autor:
De Commer, Kenny, Matassa, Marco
Publikováno v:
Advances in Mathematics, 366 (2020): 107029
Let $U$ be a connected, simply connected compact Lie group with complexification $G$. Let $\mathfrak{u}$ and $\mathfrak{g}$ be the associated Lie algebras. Let $\Gamma$ be the Dynkin diagram of $\mathfrak{g}$ with underlying set $I$, and let $U_q(\ma
Externí odkaz:
http://arxiv.org/abs/1809.08471
Autor:
Matassa, Marco
Publikováno v:
Adv. Appl. Clifford Algebras (2019) 29: 8
We classify PBW-deformations of quadratic-constant type of certain quantizations of exterior algebras. These correspond to the fundamental modules of quantum $\mathfrak{sl}_N$, their duals, and their direct sums. We show that the first two cases do n
Externí odkaz:
http://arxiv.org/abs/1710.05689
Autor:
Matassa, Marco, Yuncken, Robert
Publikováno v:
J. Noncommut. Geom. 13 (2019), 985-1009
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 obtain such a calculus is to
Externí odkaz:
http://arxiv.org/abs/1705.04178