Introduction aux méthodes euclidiennes en théorie quantique des champs
Introduction to algebra over “brave new rings”
Introduction to cochains of differential operators
Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications
These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV–formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration we present...
Introduction to noncommutative differential geometry.
Introduction to the theory of semi-holonomic jets.
Introduction to the theory of semi-holonomic jets
Invariance properties of the Laplace operator
[For the entire collection see Zbl 0699.00032.] The paper deals with a special problem of gauge theory. In his previous paper [The invariance of Sobolev spaces over noncompact manifolds, Partial differential equations, Proc. Symp., Holzhaus/GDR 1988, Teubner- Texte Math. 112, 73-107 (1989; Zbl 0681.58011)], the author introduced the Sobolev completions of the space of all G-connections on a G-principal fibre bundle P. In the present paper, under the assumption of bounded curvatures and their...
Invariant analysis and contractions of symmetric spaces : part II
Invariant analysis and contractions of symmetric spaces. Part I
Invariant Differential Operators and Polynomials of Lie Transformation Groups.
Invariant differential operators in hyperbolic spaces.
Invariant distances and invariant differential metrics in locally convex spaces
Invariant Fourier Integral Operators on Lie Groups.
Invariant functions on Lie groups and Hamiltonian flows of surface group representations.
Invariant manifolds. I.
Invariant manifolds of a differentiable vector field
Invariant measure for some differential operators and unitarizing measure for the representation of a Lie group. Examples in finite dimension
Consider a Lie group with a unitary representation into a space of holomorphic functions defined on a domain 𝓓 of ℂ and in L²(μ), the measure μ being the unitarizing measure of the representation. On finite-dimensional examples, we show that this unitarizing measure is also the invariant measure for some differential operators on 𝓓. We calculate these operators and we develop the concepts of unitarizing measure and invariant measure for an OU operator (differential operator associated to...
Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds
Invariant orders in Lie groups
[For the entire collection see Zbl 0742.00067.]The author formulates several theorems about invariant orders in Lie groups (without proofs). The main theorem: a simply connected Lie group admits a continuous invariant order if and only if its Lie algebra contains a pointed invariant cone. V. M. Gichev has proved this theorem for solvable simply connected Lie groups (1989). If is solvable and simply connected then all pointed invariant cones in are global in (a Lie wedge is said to...