Noncommutative algebraic geometry.

Laudal, Olav A.. "Noncommutative algebraic geometry.." Revista Matemática Iberoamericana 19.2 (2003): 509-580. <http://eudml.org/doc/39675>.

@article{Laudal2003,
abstract = {The need for a noncommutative algebraic geometry is apparent in classical invariant and moduli theory. It is, in general, impossible to find commuting parameters parametrizing all orbits of a Lie group acting on a scheme. When one orbit is contained in the closure of another, the orbit space cannot, in a natural way, be given a scheme structure. In this paper we shall show that one may overcome these difficulties by introducing a noncommutative algebraic geometry, where affine schemes are modeled on associative algebras. The points of such an affine scheme are the simple modules of the algebra, and the local structure of the scheme at a finite family of points, is expressed in terms of a noncommutative deformation theory proposed by the author in [10]. ...},
author = {Laudal, Olav A.},
journal = {Revista Matemática Iberoamericana},
keywords = {Geometría algebraica; Algebras no conmutativas; Algebras asociativas; deformation theory; formal methods; representation theory},
language = {eng},
number = {2},
pages = {509-580},
title = {Noncommutative algebraic geometry.},
url = {http://eudml.org/doc/39675},
volume = {19},
year = {2003},
}

TY - JOUR
AU - Laudal, Olav A.
TI - Noncommutative algebraic geometry.
JO - Revista Matemática Iberoamericana
PY - 2003
VL - 19
IS - 2
SP - 509
EP - 580
AB - The need for a noncommutative algebraic geometry is apparent in classical invariant and moduli theory. It is, in general, impossible to find commuting parameters parametrizing all orbits of a Lie group acting on a scheme. When one orbit is contained in the closure of another, the orbit space cannot, in a natural way, be given a scheme structure. In this paper we shall show that one may overcome these difficulties by introducing a noncommutative algebraic geometry, where affine schemes are modeled on associative algebras. The points of such an affine scheme are the simple modules of the algebra, and the local structure of the scheme at a finite family of points, is expressed in terms of a noncommutative deformation theory proposed by the author in [10]. ...
LA - eng
KW - Geometría algebraica; Algebras no conmutativas; Algebras asociativas; deformation theory; formal methods; representation theory
UR - http://eudml.org/doc/39675
ER -