Ryszard Nest We speci cally 1 arXiv:2106.09912v1 [math.AG] 18 Jun 2021 Noncommutative differential geometry has many actual and potential applications to several domains in physics ranging from solid state to quantization of gravity. Duke Mathematical Journal, 170(8): 1781-1850 (1 June 2021). a cohomological construction of modules over fedosov deformation quantization algebra S. A. POL'SHIN Institute for Theoretical Physics, NSC Kharkov Institute of Physics and Technology, Akademicheskaia Street 1, 61108 Kharkov, Ukraine Module im HS 20 Grundvorlesung. We also quantize involutive submanifolds of contact manifolds. Deformation Quantization of Shifted Poisson Structures. Suppose we are given complex manifolds X and Y together with substacks $\mathcal{S}$ and $\mathcal{S}'$ of modules over algebras of formal deformation $\mathcal{A}$ on X and $\mathcal{A}'$ on Y, respectively.Also, suppose we are given a functor Φ from the category of open subsets of X to the category of open subsets of Y together with a functor F of prestacks from $\mathcal{S}$ to … MAT922. IRelation with noncommutative algebras via deformation quantization (B., Waldmann, Dolgushev, Crelle’s J. North Carolina State University 2013 We adapt to the case of deformation quantization modules a formula of Lunts (Lefschetz fixed point theorems for Fourier–Mukai functors and DG algebras. We show that it is a deformation of the algebra R[V] = S(V ) of polynomial functions over V. There is a RJ~K-linear symmetrization map Sym: R[V]J~K !A ~ given by Sym(v 1v 2 v n) = 1 n! Quantum link invariants and their categorification. This paper is the continuation of arXiv:0802.1245. By Masaki Kashiwara and Pierre Schapira. analytic deformation quantization (DQ) modules on (M,ΩI) is expected to be even more tight. No action of R2 … Found inside – Page 103Preprint [GY] G. Ginot, S. Yalin, Deformation theory of bialgebras, ... 233–254 (1980) [KS] M. Kashiwara, P. Schapira, Deformation quantization modules. theorem. We are not allowed to display external PDFs yet. Found inside – Page 507[30] P. Polesello and P. Schapira, Stacks of quantization-deformation modules on com- plex symplectic manifolds. E-print (2003), to appear in Internat. However this is a new lecture, written especially for this workshop. 6 August 2020. Butthetheory ofmodules over DQ-algebroidsisalsoanatural generalization of that of D-modules. Shifted deformation quantization for a derived Artin stack endowed with a shifted Poisson structure is discussed in the last section. As a special case, we consider the parametrized strict deformation quantization of Hilbert C*-modules over C*-bundles with fibrewise torus action.Keith C. Hannabuss and Varghese Matha Probability II (Wahrscheinlichkeitstheorie) Namely, there are no instanton corrections in the Lagrangian Floer homology with boundary on I-holomorphic Lagrangians [SV19]. Strict deformation quantization of locally convex algebras and modules Gandalf Lechner and Stefan Waldmann September 2011 Abstract In this work various symbol spaces with values in a sequentially complete lo-cally convex vector space are introduced and discussed. We apply these results to the study of modules over deformation quantization algebroids on complex Poisson manifolds. Found inside – Page 305S.A. Merkulov, Lectures on PROPs, Poisson geometry and deformation quantization, Contemp. Math. 450 (2008), 223-257. S.A. Merkulov, Graph complexes with ... algebroids: an ov erview. Let X be an algebraic Poisson variety and fix a deformation quantization of the sheaf of regular functions on X. In this thesis we give conditions for a vector bundle supported on a subvariety to admit a first/second order deformation to a ... Here is the plan of my lecture: 1.Associative Deformations Found inside – Page 445Deformation quantization of Lie bialgebras produces quantum groups, which turned ... is to tensor the K-linear category of g-modules by formal power series, ... It incorporates some recent progress on the subject. to a wider class of ∗-algebras, including those arising in deformation quantization. 19. Found inside – Page 14A concise formulation of a Gerstenhaber deformation of an algebra (which we shall ... denoting by ®;, the tensor product of KHAN-modules, we can identify A ... The Lefschetz–Lunts formula for deformation quantization modules Mathematische Zeitschrift avr. Found inside – Page 37Deformation quantization modules I:Finiteness and duality. ArXiv e-prints, February 2008, 0802.1245. M. Kashiwara and P. Schapira. Deformation quantization ... We prove finiteness and duality theorems in the relative case and construct the Hochschild class of coherent modules. Abstract. We construct twisted simple holonomic modules along Λ in the stack of deformation-quantization modules on X . The dense -subalgebra A1 X m,n2Z a m,nU mVn: fa g 2S(Z2) ˆA is a strict deformation quantization of T 2associated to the natural action of R [Rieffel, 1993]. Examples and applications of representation theory Fourier series Finite-diml representations Gelfand’s abstract harmonic analysis Quadratic forms and reps of GL(n) 2. Abstract Let Λ be a smooth Lagrangian submanifold of a complex symplectic manifold X . In dimension 4k +1 some of the Lie algebras that arise have central extensions. The relationship goes through the theory of deformation quantization modules and along the way we establish a GAGA theorem for DQ modules on symplectic manifolds with a log symplectic compactification. Found inside – Page 150217 M. Kashiwara, P. Schapira, Modules over deformation quantization algebroids: An overview. Lett. Math. Phys. 88(1–3), 79–99 (2009) A. Klemm, P. Sułkowski ... The group aspect is a special case of deformation quantization and we shall show that the enveloping algebra aspect can be seen as its dual, in the sense of topological vector spaces duality. ... Poisson geometry and deformation quantization. 2012) Outline: 1.Morita equivalence reminder I: algebras. Abstract. 2 Deformation Quantization … The deformation quantization replaces the algebra of smooth functions on the Poisson manifold with the same vector space, but equipped with new noncommutative associative unital product whose commutator agrees, up to order ℏ, with the underlying Poisson bracket. We prove in particular that under a natural properness condition, the convolution of two coherent kernels over such algebroids is coherent. Found inside – Page iA"-modules,. 1993 Marc A. Rieffel, Deformation quantization for actions of R", 1993 Stephen S.-T. Yau and Yung Yu, Gorenstein quotient singularities in ... Deformation quantization of a symplectic manifold (M, w) is an as-sociative algebra (Ah, *) over C[[h]] with an isomorphism c : Ah/hAh -+ C'(M) s.t. As other methods of quantization, deformation quantization has as input a description of a classical mechanical system, which is in this case most often a smooth Poisson manifold. References. gives the decomposition of each V @n into simple modules for these representa- tions and we show that the same is true after quantization. Apply this example to the construction of deformation quantization. We consider deformation quantization of modules over O Xto modules over such O h. In characteristic zero, Gabber’s celebrated integrability of characteristics theorem implies that a coherent sheaf admitting a quanti-zation is supported on a coisotropic subvariety [Gab81]. We construct the Hochschild class for coherent modules over a deformation quantization algebroid on a complex Poisson manifold. Main Communications in Mathematical Physics Deformation Quantization of then-tuple Point Communications in Mathematical Physics 1999 / 08 Vol. Deformation Quantization in … 3.The bridge: deformation quantization 4.Morita equivalence of formal Poisson structures 66, 157–216 (2003) In characteristic 0 the picture for the categorical quantization is much Found inside – Page 96(2006) Kashiwara, M., Schapira, P.: Deformation Quantization Modules, vol. 345. Astérisque Soc. Math. France (2012). arXiv:1003.3304 Kashiwara, M., ... 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