We consider an algebraic structure of the XXZ model in the gapless regime. We argue that a certain degeneration limit of the elliptic algebra A q;p ( c sl 2 ) [5] is a relevant object. We give a free boson realization of this limiting algebra and derive an integral formula for the correlation function. The result agrees with the one obtained by solving a system of di erence equations. We also d...

We prove a strong analogue of Liouville’s Theorem in Diophantine approximation for points on arbitrary algebraic varieties. We use this theorem to prove a conjecture of the first author for cubic surfaces in P.

let $mathfrak{l}$ be the virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. we investigate the structure of the lie triplederivation algebra of $mathfrak{l}$ and $mathfrak{g}$. we provethat they are both isomorphic to $mathfrak{l}$, which provides twoexamples of invariance under triple derivation.

In this work, we are concerned with the derivation of full asymptotic expansions for Fou-rier integrals R b a f ðxÞe AEisx dx as s ? 1, where s is real positive, [a, b] is a finite interval, and the functions f(x) may have different types of algebraic and logarithmic singularities at x = a and x = b. This problem has been treated in the literature by techniques involving neu-tralizers and Melli...

Let K be an algebraic number field. Assume that ζK(s)/ζ(s) is entire. We give an explicit upper bound for the residue at s = 1 of the Dedekind zeta function ζK(s) of K. We deduce explicit upper bounds on class numbers of cubic and quartic number fields.

in this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a banach algebra $a$ into a semisimple banach algebra $b$ is continuous.

We introduce a pairing structure within the Moore complex NG of a simplicial group G and use it to investigate generators for N G n ∩ D n where D n is the subgroup generated by degenerate elements. This is applied to the study of algebraic models for homotopy types.

We prove extension results for meromorphic functions by combining the Kohn-Rossi extension theorems with Andreotti's theory on the algebraic and analytic dependence of meromorphic functions on pseudoconcave manifolds. Versions of Kohn-Rossi theorems for pseudo-convex domains are included.

Boolean functions which are simultaneously bent and negabent are studied. Transformations that leave the bent-negabent property invariant are presented. A construction for infinitely many bentnegabent Boolean functions in 2mn variables (m > 1) and of algebraic degree at most n is described, this being a subclass of the Maiorana– McFarland class of bent functions. Finally it is shown that a bent...

This work is an investigation into the structure and properties of Lie hypermatrix algebra generated by a semisimple basis. By using new algebraic tools; namely cubic hypermatrices I obtain an algebraic structure associated with the basis of a semisimple Lie algebra, and I show that the semisimple Lie basis is a generator of infinite periodic semisimple hypermatrix structures, that has a classi...