Noncommutative affine spaces and Lie-complete rings

2015-02-01
Dosi, Anar
In this paper, we investigate the structure sheaves of an (infinite-dimensional) affine NC-space A(nc)(x) affine Lie-space A(lich)(x), and their nilpotent perturbations A(nc,q)(x) and A(lich),(x)(q) respectively. We prove that the schemes A(nc)(x) and A(lich)(x) are identical if and only if x is a finite set of variables, that is, when we deal with finite-dimensional noncommutative affine spaces. For each (Zariski) open subset U subset of X = Spec(C vertical bar x vertical bar), we obtain the precise descriptions of the algebras O-nc(U), O-nc,(q)(U). O-lich,(q)(U) and O-lich,(q)(U) of noncommutative regular functions on U associated with the schemes A(nc)(x), A(nc,q)(x), A(lich),(x)(q) and respectively. The obtained result for O-nc(U) generalizes Kapranov's formula in the finite-dimensional case. Our approach to the matter is based on a noncommutative holomorphic functional calculus in Frechet algebras. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
COMPTES RENDUS MATHEMATIQUE

Suggestions

Polynomial Multiplication over Binary Fields Using Charlier Polynomial Representation with Low Space Complexity
AKLEYLEK, SEDAT; Cenk, Murat; Özbudak, Ferruh (2010-12-15)
In this paper, we give a new way to represent certain finite fields GF(2(n)). This representation is based on Charlier polynomials. We show that multiplication in Charlier polynomial representation can be performed with subquadratic space complexity. One can obtain binomial or trinomial irreducible polynomials in Charlier polynomial representation which allows us faster modular reduction over binary fields when there is no desirable such low weight irreducible polynomial in other representations. This repre...
Noncommutative Localizations of Lie-Complete Rings
Dosi, Anar (2016-01-01)
In this paper we investigate the topological localizations of Lie-complete rings. It has been proved that a topological localization of a Lie-complete ring is commutative modulo its topological nilradical. Based on the topological localizations we define a noncommutative affine scheme X = Spf (A) for a Lie-complete ring A. The main result of the paper asserts that the topological localization A((f)) of A at f is an element of A is embedded into the ring O-A (X-f) of all sections of the structure sheaf O-A o...
Nonstandard hulls of ordered vector spaces
Emelyanov, Eduard (2016-06-01)
This paper undertakes the investigation of ordered vector spaces by applying nonstandard analysis. We introduce and study two types of nonstandard hulls of ordered vector spaces. Norm-nonstandard hulls of ordered Banach spaces are also investigated.
Convex envelope results and strong formulations for a class of mixed-integer programs
Denizel, M; Erenguc, SS; Sherali, HD (1996-06-01)
In this article we present a novel technique for deriving the convex envelope of certain nonconvex fixed-charge functions of the type that arise in several related applications that have been considered in the literature. One common attribute of these problems is that they involve choosing levels for the undertaking of several activities. Two or more activities share a common resource, and a fixed charge is incurred when any of these activities is undertaken at a positive level. We consider nonconvex progra...
Nonstandard hulls of ordered vector spaces
Gül, Hasan; Emel'yanov, Eduard; Department of Mathematics (2015)
This thesis undertakes the investigation of ordered vector spaces by applying nonstandard analysis. We introduce and study two types of nonstandard hulls of ordered vector spaces. Norm-nonstandard hulls of ordered Banach spaces are also investigated
Citation Formats
A. Dosi, “Noncommutative affine spaces and Lie-complete rings,” COMPTES RENDUS MATHEMATIQUE, pp. 149–153, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63515.