Noncommutative affine spaces and Lie-complete rings

Date

2015-02-01

Author

Dosi, Anar

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

148
views

0
downloads

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.

Subject Keywords

Assocıatıve algebras, Elements

URI

https://hdl.handle.net/11511/63515

Journal

COMPTES RENDUS MATHEMATIQUE

DOI

https://doi.org/10.1016/j.crma.2014.10.020

Collections

Engineering, Article

Suggestions

OpenMETU
Core

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...
MULTINORMED W*-ALGEBRAS AND UNBOUNDED OPERATORS Dosi, Anar (2012-12-01) In this paper we investigate multinormed W*-algebras in terms of the central topologies of W*-algebras. The main result asserts that each multinormed W*-algebra can be realized as a local von Neumann algebra on a certain domain in a Hilbert space. Moreover, it admits the predual (unique up to an isometry), which is the l(1)-normed space. In the normed case the assertion is reduced to the known Sakai theorem.
Quantum system structures of quantum spaces and entanglement breaking maps Dosi, A. A. (IOP Publishing, 2019-07-01) This paper is devoted to the classification of quantum systems among the quantum spaces. In the normed case we obtain a complete solution to the problem when an operator space turns out to be an operator system. The min and max quantizations of a local order are described in terms of the min and max envelopes of the related state spaces. Finally, we characterize min-max-completely positive maps between Archimedean order unit spaces and investigate entanglement breaking maps in the general setting of quantum...
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.

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.