Related papers: A Normal form for HNN-extension of Dialgebras
Many research works have concerned normality-preserving selection rules and operations on the sequence of digits of a given normal number that maintain or violate normality. This leads us to introduce rearrangement operations on finite…
We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form. This yields, in a natural way, an explicit formula for both the Lame polynomials and the classical non-meromorphic Lame functions in terms of Chebyshev polynomials…
Anick introduced a resolution, that now bears his name, of a field using an augmented algebra over that field. We present here what one could call a dictionary between Anick's original paper and the other resources on the matter, most of…
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
We study a question which can be roughly stated as follows: Given a (unital or nonunital) algebra $A$ together with a Gr\"obner-Shirshov basis $G$, consider the free operated algebra $B$ over $A$, such that the operator satisfies some…
We develop a dimer model for the Alexander polynomial of a knot. This recovers Kauffman's state sum model for the Alexander polynomial using the language of dimers. By providing some additional structure we are able to extend this model to…
We obtain an extension of the Christoffel--Darboux formula for matrix orthogonal polynomials with a generalized Hankel symmetry, including the Adler-van Moerbeke generalized orthogonal polynomials.
We relate the counting of honeycomb dimer configurations on the cylinder to the counting of certain vertices in Kirillov-Reshetikhin crystal graphs. We show that these dimer configurations yield the quantum Kostka numbers of the small…
We address the problem of constructing the non-associative version of the Dynkin form of the Baker-Campbell-Hausdorff formula; that is, expressing $\log (\exp (x)\exp(y))$, where $x$ and $y$ are non-associative variables, in terms of the…
In this note, we observe a relation between dialgebras (in particular, Leibniz algebras) and conformal algebras. The purpose is to show how the methods of conformal algebras help solving problems on dialgebras, and, conversely, how the…
We consider the quadratic derivative nonlinear Schr\"odinger equation (dNLS) on the circle. In particular, we develop an infinite iteration scheme of normal form reductions for dNLS. By combining this normal form procedure with the…
An algebraic deformation theory of dialgebra morphisms is obtained.
We obtain Hamel--Goulden-type ribbon decomposition determinantal formulas for flagged supersymmetric Schur functions. As an application, we derive corresponding new determinantal formulas dual refined canonical stable Grothendieck…
We introduce and study a generalized form of derivations for dendriform algebras, specifying all admissible parameter values that define these derivations. Additionally, we present a complete classification of generalized derivations for…
We give a uniform interpretation of the classical continuous Chebyshev's and Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie algebra gl(N), where N is any complex number. One can similarly interpret Chebyshev's…
This chapter of the proceedings for the Ninth Meeting on CPT and Lorentz Symmetry is dedicated to the Hamiltonian formulation of the minimal gravitational Standard-Model Extension. Some theoretical questions associated with the latter shall…
Let K be a finite Galois extension of Q. The normal basis theorem provides an element of K whose conjugates form a Q-basis of K. Here we obtain such an element with controlled size. This improves a recent result by Fukshansky and Jeong. By…
This paper studies the seminormal bases $\{f_{\mathfrak{s}\mathfrak{t}}\}$ and the dual seminormal bases $\{g_{\mathfrak{s}\mathfrak{t}}\}$ of the non-degenerate and the degenerate cyclotomic Hecke algebras ${H}_{\ell,n}$ of type…
In this paper we establish a Gr\"{o}bner-Shirshov bases theory for Lie algebras over commutative rings. As applications we give some new examples of special Lie algebras (those embeddable in associative algebras over the same ring) and…
The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…