Field theory on curved noncommutative spacetimes.
Formal deformations and principal series representations of and
In this note, we study formal deformations of derived representations of the principal series representations of . In particular, we recover all the representations of the derived principal series by deforming one of them. Similar results are also obtained for .
Formal Lagrangian operad.
Formality theorems: from associators to a global formulation
Let be a differential manifold. Let be a Drinfeld associator. In this paper we explain how to construct a global formality morphism starting from . More precisely, following Tamarkin’s proof, we construct a Lie homomorphism “up to homotopy" between the Lie algebra of Hochschild cochains on and its cohomology ). This paper is an extended version of a course given 8 - 12 March 2004 on Tamarkin’s works. The reader will find explicit examples, recollections on -structures, explanation of the...
GAGA for DQ-algebroids
Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects
We shall give a survey of classical examples, together with algebraic methods to deal with those structures: graded algebra, cohomologies, cohomology operations. The corresponding geometric structures will be described(e.g., Lie algebroids), with particular emphasis on supergeometry, odd supersymplectic structures and their classification. Finally, we shall explain how BV-structures appear in Quantum Field Theory, as a version of functional integral quantization.
Higher symmetries of the Laplacian via quantization
We develop a new approach, based on quantization methods, to study higher symmetries of invariant differential operators. We focus here on conformally invariant powers of the Laplacian over a conformally flat manifold and recover results of Eastwood, Leistner, Gover and Šilhan. In particular, conformally equivariant quantization establishes a correspondence between the algebra of Hamiltonian symmetries of the null geodesic flow and the algebra of higher symmetries of the conformal Laplacian. Combined...
Hochschild cohomology and deformations of Clifford-Weyl algebras.
Hochschild cohomology theories in white noise analysis.
Hochschild homology and cohomology of Klein surfaces.
Hochshild cohomology and equivalence of graded star products.
Introduction to noncommutative differential geometry.
-star products on dual of Lie algebras.
Kontsevich quantization and invariant distributions on Lie groups
Linearization and star products
The aim of this paper is to give an overview concerning the problem of linearization of Poisson structures, more precisely we give results concerning Poisson-Lie groups and we apply those cohomological techniques to star products.
Moving frames, Geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors
In this paper we describe a non-local moving frame along a curve of pure spinors in , and its associated basis of differential invariants. We show that the space of differential invariants of Schwarzian-type define a Poisson submanifold of the spinor Geometric Poisson brackets. The resulting restriction is given by a decoupled system of KdV Poisson structures. We define a generalization of the Schwarzian-KdV evolution for pure spinor curves and we prove that it induces a decoupled system of KdV...
On category for cyclotomic rational Cherednik algebras
We study equivalences for category of the rational Cherednik algebras of type : a highest weight equivalence between and for and an action of on an explicit non-empty Zariski open set of parameters ; a derived equivalence between and whenever and have integral difference; a highest weight equivalence between and a parabolic category for the general linear group, under a non-rationality assumption on the parameter . As a consequence, we confirm special cases of conjectures...
On Hopf algebra deformation approach to renormalization.
On Martin Bordemann's proof of the existence of projectively equivariant quantizations
The paper explains the notion of projectively equivariant quantization. It gives a sketch of Martin Bordemann's proof of the existence of projectively equivariant quantization on arbitrary manifolds.
On the index theorem for symplectic orbifolds
We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula.