Related papers: A class of Baker-Akhiezer arrangements

In this paper we classify, up to analytic isomorphism, the family of almost stretched Artinian complete intersection A=R/I with a given Hilbert function, in the case R is a power series ring with an arbitrary number of variables.

This note is a contribution to large scale geometry. More precisely, we introduce the intrinsically quasi-isometric sections in metric spaces and we investigate their properties: the Ahlfors-David regularity in large scale; following…

This is a revised and corrected version of a preprint circulated in 1990 in which various non-self-adjoint limit algebras are classified. The principal invariant is the scaled $K_0$ group together with the algebraic order on the scale…

We introduce a new class of symmetric algebras, which we call hybrid algebras. This class contains on one extreme Brauer graph algebras, and on the other extreme general weighted surface algebras. We show that hybrid algebras are precisely…

All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by I. Shirokov. The varieties of the deformed Galilei algebras are discussed and families of…

We study invariant pseudo-K\"ahler structures on a solvmanifold $G$ such that the Lie algebra $\mathfrak{g}$ is almost abelian, that is $\mathfrak{g}=\mathfrak{h}\rtimes\mathbb{R}$, with $\mathfrak{h}$ abelian; comparing with the…

We introduce and study the notion of affine varieties associated to ordered bases and establish Galois connection between the power set of $A^n_K$ and the power set of $K[x_1, . . ., x_n]$, and then induce a Galois correspondence. We…

We explore algebraic relations on Vassiliev knot invariants related with correlators in the 3-dimensional Chern--Simons theory. Vassiliev invariants form infinite-dimensional algebra. We focus on $k$-parametric knot families with Vassiliev…

The classification of local Artinian Gorenstein algebras is equivalent to the study of orbits of a certain non-reductive group action on a polynomial ring. We give an explicit formula for the orbits and their tangent spaces. We apply our…

This paper presents a solution to a problem from superanalysis about the existence of Hilbert-Banach superalgebras. Two main results are derived: 1) There exist Hilbert norms on some graded algebras (infinite-dimensional superalgebras…

This paper studies a new class of integration schemes for the numerical solution of semi-explicit differential-algebraic equations of differentiation index 2 in Hessenberg form. Our schemes provide the flexibility to choose different…

We study the weak Lefschetz property of artinian Gorenstein algebras and in particular of artinian complete intersections. In codimension four and higher, it is an open problem whether all complete intersections have the weak Lefschetz…

A basis of quasi-invariant module over invariants is explicitly constructed for the two-dimensional Coxeter systems with arbitrary multiplicities. It is proved that this basis consists of $m$-harmonic polynomials, thus the earlier results…

The paper presents two new results concerning the varieties of Leibnitz algebras. We find values of multiplicities and colength variety of Leibniz algebras of almost polynomial growth, which is generated by the algebra constructed with the…

We study a physically motivated representation of an algebra of operators in gravitational and non gravitational theories called the covariant representation of an algebra. This is a representation where the symmetries of the operator…

We construct a version of Beilinson's regulator as a map of sheaves of commutative ring spectra and use it to define a multiplicative variant of differential algebraic K-theory. We use this theory to give an interpretation of Bloch's…

We define the concept of higher order differential operators on a general noncommutative, nonassociative superalgebra A, and show that a vertex operator superalgebra has plenty of them, namely modes of vertex operators. A linear operator…

We prove upper bounds for the Hilbert-Samuel multiplicity of standard graded Gorenstein algebras. The main tool that we use is Boij-S\"oderberg theory to obtain a decomposition of the Betti table of a Gorenstein algebra as the sum of…

Let E be an operator algebra on a Hilbert space with finite-dimensional generated C*-algebra. A classification is given of the locally finite algebras and the operator algebras obtained as limits of direct sums of matrix algebras over E…

We discuss the conjecture of Buchstaber and Krichever that their multi-dimensional vector addition formula for Baker-Akhiezer functions characterizes Jacobians among principally polarized abelian varieties, and prove that it is indeed a…