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See detailAlmost Commutative Q-algebras and Derived brackets
Bruce, Andrew UL

in Journal of Noncommutative Geometry (in press)

We introduce the notion of almost commutative Q-algebras and demonstrate how the derived bracket formalism of Kosmann-Schwarzbach generalises to this setting. In particular, we construct ‘almost ... [more ▼]

We introduce the notion of almost commutative Q-algebras and demonstrate how the derived bracket formalism of Kosmann-Schwarzbach generalises to this setting. In particular, we construct ‘almost commutative Lie algebroids’ following Vaintrob’s Q-manifold understanding of classical Lie algebroids. We show that the basic tenets of the theory of Lie algebroids carry over verbatim to the almost commutative world. [less ▲]

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See detailQuantization of spectral curves and DQ-modules
Petit, François UL

in Journal of Noncommutative Geometry (2018)

Given an holomorphic Higgs bundle on a compact Riemann surface of genus greater than one, we prove the existence of an holonomic DQ-module supported by the spectral curve associated to this bundle. Then ... [more ▼]

Given an holomorphic Higgs bundle on a compact Riemann surface of genus greater than one, we prove the existence of an holonomic DQ-module supported by the spectral curve associated to this bundle. Then, we relate quantum curves arising in various situations (quantization of spectral curves of Higgs Bundles, quantization of the A-polynomial...) to DQ-modules and show that a quantum curve and the DQ-module canonically associated to it have isomorphic sheaves of solutions. [less ▲]

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See detailModuli stacks of algebraic structures and deformation theory
Yalin, Sinan UL

in Journal of Noncommutative Geometry (2016)

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See detailGrothendieck-Teichmueller group and Poisson cohomologies
Alm, Johan; Merkulov, Sergei UL

in Journal of Noncommutative Geometry (2015), 9(1), 185-214

We study actions of the Grothendieck–Teichmüller group GRT on Poisson cohomologies of Poisson manifolds, and prove some “go” and “no-go” theorems associated with these actions.

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See detailModuli stacks of algebraic structures and deformation theory
Yalin, Sinan UL

in Journal of Noncommutative Geometry (2015)

Detailed reference viewed: 70 (1 UL)