Related papers: Analytic integrability around a nilpotent singular…

The index of a Lie algebra is an important invariant which arises in several areas, e.g. in the study of coadjoint orbits for a Lie group, in invariant theory and in representation theory. We study the index for several classes of nilpotent…

We point out that some of the proposed generalized/modified uncertainty principles originate from solvable, or nilpotent at appropriate limits, "deformations" of Lie algebras. We briefly comment on formal aspects related to the…

An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut

We provide a nilpotency criterion for fusion systems in terms of the vanishing of its cohomology with twisted coefficients.

In this paper we solve the problem of analytic classification of plane curves singularities with two branches by presenting their normal forms. This is accomplished by means of a new analytic invariant that relates vectors in the tangent…

We extend a result proved in \cite{Col} for mirror symmetries of planar systems to measure-preserving non-linear reversibilities of $n$-dimensional systems, dropping the analyticity and nondegeneracy conditions.

Let A be an associative algebra of arbitrary dimension over a field F and G a finite soluble group of automorphisms of A oforder n, prime to the characteristic of F. We prove that if the fixed-point subalgebra of A under the action of G…

It is shown that any finite-dimensional homomorphic image of an inverse limit of nilpotent not-necessarily-associative algebras over a field is nilpotent. More generally, this is true of algebras over a general commutative ring k, with…

In this article we study the homology of nilpotent groups. In particular a certain vanishing result for the homology and cohomology of nilpotent groups is proved.

The notion of analyticity is studied in the context of hypercomplex numbers. A critical review of the problems arising from the conventional approach is given. We describe a local analyticity condition which yields the desired type of…

The dual complex associated to a resolution of singularities generalizes the notion of a resolution graph of a surface singularity to any dimension. We show that homotopy type of the dual complex is an invariant of an isolated singularity.

We investigate the Dirichlet solution for a semianalytic continuous function on the boundary of a semianalytic bounded domain in the plane. We show that the germ of the Dirichlet solution at a boundary point with angle greater than 0 lies…

Writing the boundary integral equation for an exterior problem of elasticity is subordinate so far to hypotheses on the asymptotical behaviour at infinity of solutions. The sufficient conditions met in the literature are too restrictive and…

In this paper we study gradings on simple Lie algebras arising from nilpotent elements. Specifically, we investigate abelian subalgebras which are degree 1 homogeneous with respect to these gradings. We show that for each odd nilpotent…

Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value…

This paper investigates some properties of complex structures on Lie algebras. In particular, we focus on $\textit{nilpotent}$ $\textit{complex structures}$ that are characterized by a suitable $J$-invariant ascending or descending central…

An infinite family of exactly-solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular…

In this paper, we study simplicial commutative algebras with finite Andr\'e-Quillen homology. Here we restrict our focus to simplicial algebras having characteristic 2. Our aim is to find a generalization of results established by the…

In this paper we consider the problem of quantizing theories defined over configuration spaces described by non-commuting parameters. If one tries to do that by generalizing the path-integral formalism, the first problem one has to deal…

For differential inequalities with the $\infty$-Laplacian in the principal part, we obtain conditions for the absence of solutions in unbounded domains. Examples are given to demonstrate the accuracy of these conditions.