Related papers: Formal conjugacy and asymptotic differential algeb…
We study the scheme of formal arcs on a singular algebraic variety and its images under truncations. We prove a rationality result for the Poincare series of these images which is an analogue of the rationality of the Poincare series…
We investigate higher-order asymptotic symmetries for a $p$-form gauge field in $(p + 2)$-dimensional Minkowski spacetime, where Hodge duality with a scalar holds. Employing symplectic renormalization, we identify $N + 1$ independent…
We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…
We investigate the structure of the centralizer and the normalizer of a local analytic or formal differential system at a nondegenerate stationary point, using the theory of Poincar\'e-Dulac normal forms. Our main results are concerned with…
Over a field of characteristic zero we prove two formality conditions. We prove that a dg Lie algebra is formal if and only if its universal enveloping algebra is formal. We also prove that a commutative dg algebra is formal as a dg…
For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…
We give a natural definition of a Poisson Differential Algebra. Consistence conditions are formulated in geometrical terms. It is found that one can often locally put the Poisson structure on differential calculus in a simple canonical form…
We study asymptotics of integrals of certain rational functions that depend on parameters in a field $K$ of characteristic zero. We use formal power series to represent the integral and prove certain identities about its coefficients…
We study differential equations $F(y,...,y^{(n)})=0$ where $F(Y_0,...,Y_n)$ is a formal series in $Y_0,...,Y_n$ with coefficients in some field of \emph{generalized power series} $\mathds{K}_r$ with finite rank $r\in\mathbb{N}^*$. Our…
We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…
Let $k$ be an algebraically closed field of characteristic zero, and $k[[z]]$ the ring of formal power series over $k$. In this paper, we study equations in the semigroup $z^2k[[z]]$ with the semigroup operation being composition. We prove…
We construct N-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ generalizing thereby the usual complex (N=2) of differential forms. These complexes arise naturally in the description of higher spin gauge…
We study formal power series which can be interpreted as interpolations of Fibonacci and Lucas polynomials with even (or odd) indices.
Using topological methods, we study the structure of the set of forced oscillations of a class of parametric, implicit ordinary differential equations with a generalized $\Phi$-Laplacian type term. We work in the Carath\'eodory setting.…
We consider a differential algebra F of formal power series in infinitely many variables. We define the important notions of a normalized set of generators for an ideal of F and a regular quotient algebra. The concept of the passive…
A new deformed canonical commutation relation, generalizing various known deformations, is defined together with its structure function of deformation. Then, the related irreducible representations are characterized and classified. Finally,…
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…
The algebra and calculus of generalized differential forms are reviewed and employed to construct a class of generalized connections and to investigate their properties. The class includes generalized connections which are flat when…
We establish a correspondence between automorphisms and derivations on certain algebras of generalised power series. In particular, we describe a Lie algebra of derivations on a field $k(\!(G)\!)$ of generalised power series, exploiting our…
We study a family of interacting bosonic representations of the N=2 superconformal algebra. These models can be tensored with a conjugate theory to give the free theory. We explain how to use free fields to study interacting fields and…