Related papers: Algebraic method of group classification for semi-…
This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we extend the classical notion of a dg-algebra…
In this article, we address the classification of smooth projective algebraic surfaces over complex numbers admitting algebraic semigroup structures. We give a full description of those surfaces $S$, which has at least one non-trivial…
Various partially ordered Grothendieck group invariants are introduced for general operator algebras and these are used in the classification of direct systems and direct limits of finite-dimensional complex incidence algebras with common…
This paper deals with the approximation of the spectrum of linear and nonautonomous delay differential equations through the reduction of the relevant evolution semigroup from infinite to finite dimension. The focus is placed on classic…
We demonstrate the systematic derivation of a class of discretizations of nonlinear Schr{\"o}dinger (NLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic condition. We…
Schr\"odinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to…
The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups…
This is an introduction to linear algebra and group theory. We first review the linear algebra basics, namely the determinant, the diagonalization procedure and more, and with the determinant being constructed as it should, as a signed…
Kinematical invariance groups of the 3d Schr\"odinger equations with position dependent masses (PDM) and arbitrary potentials are classified. It is shown that there exist 94 classes of such equations defined up to the generic equivalence…
We analyse a class of time discretizations for solving the nonlinear Schr\"odinger equation with non-smooth potential and at low-regularity on an arbitrary Lipschitz domain $\Omega \subset \mathbb{R}^d$, $d \le 3$. We show that these…
Several relations and bounds for the dimension of principal ideals in group algebras are determined by analyzing minimal polynomials of regular representations. These results are used in the two last sections. First, in the context of…
We extend the family of classical Schur algebras in type A, which determine the polynomial representation theory of general linear groups over an infinite field, to a larger family, the rational Schur algebras, which determine the rational…
For the family of nonlinear Schr\"odinger equations derived by H.-D.~Doebner and G.A.~Goldin (J.Phys.A 27, 1771) we calculate the complete set of Lie symmetries. For various subfamilies we find different finite and infinite dimensional Lie…
In this paper we introduce a new approach for organizing algebras of global dimension at most 2. We introduce the notion of cluster equivalence for these algebras, based on whether their generalized cluster categories are equivalent. We are…
General solutions of nonlinear ordinary differential equations (ODEs) are in general difficult to find although powerful integrability techniques exist in the literature for this purpose. It has been shown that in some scalar cases…
The enhanced group classification of a semi-linear generalization of a general bond-pricing equation is carried out by employing the underlying equivalence and additional equivalence transformations. The knowledge of the sub classes with…
Computation of polynomial relative invariants is a classical tool in algebra. Relative differential invariants are central for the equivalence problem of geometric structures. We address the fundamental problem of finite generation of their…
We develop and study the generalization of rational Schur algebras to the super setting. Similar to the classical case, this provides a new method for studying rational supermodules of the general linear supergroup $GL(m|n)$. Furthermore,…
We study the category $\mathcal{A}$ of smooth semilinear representations of the infinite symmetric group over the field of rational functions in infinitely many variables. We establish a number of results about the structure of…
We present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-)acylindrically on finite products of $\delta$-hyperbolic spaces with general type factors. Inspired by the classical theory of…