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We suggest a way to quantize, using Berezin-Toeplitz quantization, a compact hyperkahler manifold (equipped with a natural 3-plectic form), or a compact integral Kahler manifold of complex dimension n regarded as a (2n-1)-plectic manifold.
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F. Bayen, M. Flato · 1975
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F. Berezin · 1975
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N. Mukunda, E. Sudarshan · 1976
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Toeplitz quantization of Kähler manifolds and gl(N), N → ∞ N\to\infty limits
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R. Ibàñez, M. de León, J. Marrero, D. Martín de Diego · 1997
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Identities for the ternary commutator
M. Bremner · 1998
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On the geometry of multisymplectic manifolds
F. Cantrijn, A. Ibort, M. de León · 1999
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Hyperkahler manifolds
M. Verbitsky, D. Kaledin · 1999
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A survey on Nambu-Poisson brackets
I. Vaisman · 1999
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Deformation quantization of compact Kähler manifolds by Berezin-Toeplitz quantization
M. Schlichenmaier · 2000
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Identification of Berezin-Toeplitz deformation quantization
A. Karabegov, M. Schlichenmaier · 2001
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Classical and quantum Nambu mechanics
n-ary algebras: a review with applications
J. A. de Azcárraga, J. M. Izquierdo · 2010
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Categorified symplectic geometry and the classical string
J. Baez, A. Hoffnung, C. Rogers · 2010
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Categorified symplectic geometry and the string Lie 2-algebra
J. Baez, C. Rogers · 2010
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Quantized Nambu-Poisson manifolds and n-Lie algebras
J. DeBellis, C. Sämann, R. Szabo · 2010
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Hyperkähler manifolds and sheaves
D. Huybrechts · 2010
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Berezin-Toeplitz quantization for compact Kähler manifolds. A review of results
M. Schlichenmaier · 2010
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J. Andersen · 2006
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Holomorphic Morse inequalities and Bergman kernels
X.Ma, G. Marinescu · 2007
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X.Ma, G. Marinescu · 2011
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Multi-moment maps
T. Madsen, A. Swann · 2012
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Quantum unsharpness and symplectic rigidity
L. Polterovich · 2012
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L ∞ L_{\infty} -algebras from multisymplectic geometry
C. Rogers · 2012
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The Cauchy problem for the homogeneous Monge-Ampère equation, I. Toeplitz quantization
Y. Rubinstein, S. Zelditch · 2012
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C. Rogers · 2013
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Groupoids, loop spaces and quantization of 2-plectic manifolds
C. Sämann, R. Szabo · 2013
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Semi-classical properties of Berezin-Toeplitz operators with C k C^{k} -symbol
T. Barron, X. Ma, G. Marinescu, M. Pinsonnault · 2014
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