Modèle de Whittaker et ideaux primitifs complètement premiers dans les algèbres enveloppantes des algèbres de Lie semisimples complexes II.
One-dimensional infinitesimal-birational duality through differential operators
The structure of filtered algebras of Grothendieck's differential operators on a smooth fat point in a curve and graded Poisson algebras of their principal symbols is explicitly determined. A related infinitesimal-birational duality realized by a Springer type resolution of singularities and the Fourier transformation is presented. This algebro-geometrical duality is quantized in appropriate sense and its quantum origin is explained.
Poincaré duality for - Lie superalgebras
Présentation jordanienne de l'algèbre de Weyl A₂
Let k be a commutative field. For any a,b∈ k, we denote by the deformation of the 2-dimensional Weyl algebra over k associated with the Jordanian Hecke symmetry with parameters a and b. We prove that: (i) any can be embedded in the usual Weyl algebra A₂(k), and (ii) is isomorphic to A₂(k) if and only if a = b.
Primitivity in skew Laurent polynomial rings and related rings.
Quantization of canonical cones of algebraic curves
We introduce a quantization of the graded algebra of functions on the canonical cone of an algebraic curve , based on the theory of formal pseudodifferential operators. When is a complex curve with Poincaré uniformization, we propose another, equivalent construction, based on the work of Cohen-Manin-Zagier on Rankin-Cohen brackets. We give a presentation of the quantum algebra when is a rational curve, and discuss the problem of constructing algebraically “differential liftings”.
Quantization of the Marsden-Weinstein reduction for extended Dynkin quivers
Rings of differential operators over rational affine curves
Some examples of nil Lie algebras
Generalizing Petrogradsky’s construction, we give examples of infinite-dimensional nil Lie algebras of finite Gelfand–Kirillov dimension over any field of positive characteristic.
Spectrum of the quantized Weyl algebra. (Spectre de l'algèbre de Weyl quantique.)
Tauvel's height formula in iterated differential operator rings.
The characteristic variety of a generic foliation
We confirm a conjecture of Bernstein–Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.
The kernel of an homomorphism of Harish-Chandra
Truncated microsupport and holomorphic solutions of D-modules
Дифференциальные алгебры и законы сохранения низших размерностей
Об одной реализации свободной алгебры Ли
Сложность решения систем линейных уравнений в кольцах дифференциальных операторов