Related papers: Algebraic Birkhoff Factorization and the Euler-Mac…

Grothendieck-Birkhoff Theorem states that every finite dimensional vector bundle over the projective line P1 splits as the sum of one dimensional vector bundles. This can be rephrased, in terms of orders, as stating that all maximal orders…

We present an integral formula for the universal R-matrix of quantum affine algebra with 'Drinfeld comultiplication'. We show that the properties of the universal R-matrix follow from the factorization properties of the cycles in proper…

Fixing an arithmetic lattice $\Gamma$ in an algebraic group $G$, the commensurability growth function assigns to each $n$ the cardinality of the set of subgroups $\Delta$ with $[\Gamma : \Gamma \cap \Delta] [\Delta: \Gamma \cap \Delta] =…

In a capacitated directed graph, it is known that the set of all min-cuts forms a distributive lattice [1], [2]. Here, we describe this lattice as a regular predicate whose forbidden elements can be advanced in constant parallel time after…

We consider Euclidean lattices spanned by images of algebraic conjugates of an algebraic number under Minkowski embedding, investigating their rank, properties of their automorphism groups and sets of minimal vectors. We are especially…

This paper announces results on the behavior of some important algebraic and topological invariants --- Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. --- and their associated…

The problem of minimizing an integral functional of a vector-valued Lagrangian on a set of admissible arcs with given endpoints is considered. The problem is tackled by embedding it into a set-optimization problem such that the image space…

Let $\mathfrak{g}$ be a Leibniz algebra and $E$ a vector space containing $\mathfrak{g}$ as a subspace. All Leibniz algebra structures on $E$ containing $\mathfrak{g}$ as a subalgebra are explicitly described and classified by two…

We define a canonical relative commutant planar algebra from a strongly Markov inclusion of finite von Neumann algebras. In the case of a connected unital inclusion of finite dimensional C*-algebras with the Markov trace, we show this…

We analyze the factorization process for lattice maps, searching for integrable cases. The maps were assumed to be at most quadratic in the dependent variables, and we required minimal factorization (one linear factor) after 2 steps of…

In this paper we develop a Morse-like theory in order to decompose birational maps and morphisms of smooth projective varieties defined over a field of characteristic zero into more elementary steps which are locally \'etale isomorphic to…

This work extends the factorization method to the inverse scattering problem of reconstructing the shape and location of an absorbing penetrable scatterer embedded in a thin infinite elastic (Kirchhoff--Love) plate. With the assumption that…

A Dirac comb of point measures in Euclidean space with bounded complex weights that is supported on a lattice inherits certain general properties from the lattice structure. In particular, its autocorrelation admits a factorization into a…

Let $V$ be a two-dimensional vector space over a field $\mathbb F$ of characteristic not $2$ or $3$. We show there is a canonical surjection $\nu$ from the set of suitably generic commutative algebra structures on $V$ modulo the action of…

We show an equation of Euler characteristics of tautological sheaves on Hilbert schemes of points on the fibers of a double point degeneration. This equation resembles a computation of such Euler characteristics via a combinatorial…

We prove a noncommutative Bader-Shalom factor theorem for lattices with dense projections in product groups. As an application of this result and our previous works, we obtain a noncommutative Margulis factor theorem for all irreducible…

Generalizing the notion of a multiplicative inequality among minors of a totally positive matrix, we describe, over full rank cluster algebras of finite type, the cone of Laurent monomials in cluster variables that are bounded as a…

We give normal forms of determinantal representations of a smooth projective plane cubic in terms of Moore matrices. Building on this, we exhibit matrix factorizations for all indecomposable vector bundles of rank 2 and degree 0 without…

Starting with a finite-dimensional complex Lie algebra, we extend scalars using suitable commutative topological algebras. We study Birkhoff decompositions for the corresponding loop groups. Some results remain valid for loop groups with…

In this paper we focus on a certain self-distributive multiplication on coalgebras, which leads to so-called rack bialgebra. We construct canon-ical rack bialgebras (some kind of enveloping algebras) for any Leibniz algebra. Our motivation…