scholarly journals Classification of Equivariant Star Products on Symplectic Manifolds

2016 ◽  
Vol 106 (5) ◽  
pp. 675-692 ◽  
Author(s):  
Thorsten Reichert ◽  
Stefan Waldmann
Keyword(s):  
Symplectic Manifolds ◽  
Star Products

scholarly journals Classification of Invariant Star Products up to Equivariant Morita Equivalence on Symplectic Manifolds

2011 ◽  
Vol 100 (2) ◽  
pp. 203-236 ◽  
Author(s):  
Stefan Jansen ◽  
Nikolai Neumaier ◽  
Gregor Schaumann ◽  
Stefan Waldmann
Keyword(s):  
Symplectic Manifolds ◽  
Morita Equivalence ◽  
Star Products

scholarly journals The tropical momentum map: a classification of toric log symplectic manifolds

2016 ◽  
Vol 367 (3-4) ◽  
pp. 1217-1258 ◽  
Author(s):  
Marco Gualtieri ◽  
Songhao Li ◽  
Álvaro Pelayo ◽  
Tudor S. Ratiu
Keyword(s):  
Symplectic Manifolds ◽  
Momentum Map

scholarly journals QUANTUM MOMENT MAPS AND INVARIANTS FOR G-INVARIANT STAR PRODUCTS

2002 ◽  
Vol 14 (06) ◽  
pp. 601-621 ◽  
Author(s):  
KENTARO HAMACHI
Keyword(s):  
Symplectic Manifold ◽  
Moment Map ◽  
New Method ◽  
Star Products ◽  
Moment Maps

We study a quantum moment map and propose an invariant for G-invariant star products on a G-transitive symplectic manifold. We start by describing a new method to construct a quantum moment map for G-invariant star products of Fedosov type. We use it to obtain an invariant that is invariant under G-equivalence. In the last section we give two simple examples of such invariants, which involve non-classical terms and provide new insights into the classification of G-invariant star products.

scholarly journals Classification of six-dimensional monotone symplectic manifolds admitting semifree circle actions I

2019 ◽  
Vol 30 (06) ◽  
pp. 1950032 ◽  
Author(s):  
Yunhyung Cho
Keyword(s):  
Symplectic Manifold ◽  
Symplectic Manifolds ◽  
Complete List ◽  
Fano Manifold ◽  
Fano Manifolds ◽  
Circle Actions ◽  
Isolated Point

Let [Formula: see text] be a six-dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian [Formula: see text]-action. We show that if the minimal (or maximal) fixed component of the action is an isolated point, then [Formula: see text] is [Formula: see text]-equivariantly symplectomorphic to some Kähler Fano manifold [Formula: see text] with a certain holomorphic [Formula: see text]-action. We also give a complete list of all such Fano manifolds and describe all semifree [Formula: see text]-actions on them specifically.

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