相关论文: The first Pontryagin class

We introduce a new class of graded rings extending the class of generalized Weyl algebras. These rings are orders in crossed products of the most general type, and we introduce their basic structure theory. We provide an extensive list of…

In this note we determine the obstruction to triviality of the stack of exact vertex algebroids.

This article provides a pedagogical introduction to the basic concepts of chiral perturbation theory and is designed as a text for a two-semester course on that topic. Chapter 1 serves as a general introduction to the empirical and…

In this paper we proved a theorems of existence and uniqueness of solutions of differential equation of second order with fractional derivative in the Kipriyanov sense in lower terms. As a domain of definition of the functions we consider…

We begin by considering faithful matrix representations of elementary abelian groups in prime characteristic. The representations considered are seen to be determined up to change of bases by a single number. Studying this number leads to a…

The goal of this paper is to set up an obstruction theory in the context of algebras over an operad and in the framework of differential graded modules over a field. Precisely, the problem we consider is the following: Suppose given two…

In this paper we classify the finite-dimensional pointed rank one Hopf algebras which are generated as algebras by the first element of the coradical filtration over a field of prime characteristic.

We study the algebras generated by restriction and induction operations on complex modules over dihedral groups. In the case where the orders of all dihedral groups involved are not divisible by four, we describe the relations, a basis, the…

The integrability problem consists in finding the class of functions a first integral of a given planar polynomial differential system must belong to. We recall the characterization of systems which admit an elementary or Liouvillian first…

In this note we study systems with a closed algebra of second class constraints. We describe a construction of the reduced theory that resembles the conventional treatment of first class constraints. It suggests, in particular, to compute…

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…

In this paper we exhibit and study a novel class of exceptional Krall orthogonal polynomials of Hermite type. This means that the polynomials in question are (i) orthogonal with respect to a Hermite-type weight; (ii) are the eigenfunctions…

In this paper we introduce toric rings of multicomplexes. We show how to compute the divisor class group and the class of the canonical module when the toric ring is normal. In the special case that the multicomplex is a discrete…

Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…

Textbook treatments of classical mechanics typically assume that the Lagrangian is nonsingular. That is, the matrix of second derivatives of the Lagrangian with respect to the velocities is invertible. This assumption insures that (i)…

The Dirac equation with chiral symmetry is derived using the irreducible representations of the Poincar\'{e} group, the Lagrangian formalism, and a novel method of projection operators that takes as its starting point the minimal assumption…

The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be…

We introduce the notion of a conformal de Rham complex of a Riemannian manifold. This is a graded differential Banach algebra and it is invariant under quasiconformal maps, in particular the associated cohomology is a new quasiconformal…

We utilize group-theoretical methods to develop a matrix representation of differential operators that act on tensors of any rank. In particular, we concentrate on the matrix formulation of the curl operator. A self-adjoint matrix of the…

Based on the ideas of Cuntz and Quillen, we give a simple construction of cyclic homology of unital algebras in terms of the noncommutative de Rham complex and a certain differential similar to the equivariant de Rham differential. We…