Quantum sections and Gauge algebras.

Lieven Le Bruyn; Freddy van Oystaeyen

Publicacions Matemàtiques (1992)

  • Volume: 36, Issue: 2A, page 693-714
  • ISSN: 0214-1493

Abstract

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Using quantum sections of filtered rings and the associated Rees rings one can lift the scheme structure on Proj of the associated graded ring to the Proj of the Rees ring. The algebras of interest here are positively filtered rings having a non-commutative regular quadratic algebra for the associated graded ring; these are the so-called gauge algebras obtaining their name from special examples appearing in E. Witten's gauge theories. The paper surveys basic definitions and properties but concentrates on the development of several concrete examples.

How to cite

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Le Bruyn, Lieven, and Oystaeyen, Freddy van. "Quantum sections and Gauge algebras.." Publicacions Matemàtiques 36.2A (1992): 693-714. <http://eudml.org/doc/41746>.

@article{LeBruyn1992,
abstract = {Using quantum sections of filtered rings and the associated Rees rings one can lift the scheme structure on Proj of the associated graded ring to the Proj of the Rees ring. The algebras of interest here are positively filtered rings having a non-commutative regular quadratic algebra for the associated graded ring; these are the so-called gauge algebras obtaining their name from special examples appearing in E. Witten's gauge theories. The paper surveys basic definitions and properties but concentrates on the development of several concrete examples.},
author = {Le Bruyn, Lieven, Oystaeyen, Freddy van},
journal = {Publicacions Matemàtiques},
keywords = {filtered rings; associated graded rings; commutative Noetherian domains; schemes; quantum sections; non-commutative quadratic Auslander-regular algebras; gauge algebras; survey; associated Rees rings},
language = {eng},
number = {2A},
pages = {693-714},
title = {Quantum sections and Gauge algebras.},
url = {http://eudml.org/doc/41746},
volume = {36},
year = {1992},
}

TY - JOUR
AU - Le Bruyn, Lieven
AU - Oystaeyen, Freddy van
TI - Quantum sections and Gauge algebras.
JO - Publicacions Matemàtiques
PY - 1992
VL - 36
IS - 2A
SP - 693
EP - 714
AB - Using quantum sections of filtered rings and the associated Rees rings one can lift the scheme structure on Proj of the associated graded ring to the Proj of the Rees ring. The algebras of interest here are positively filtered rings having a non-commutative regular quadratic algebra for the associated graded ring; these are the so-called gauge algebras obtaining their name from special examples appearing in E. Witten's gauge theories. The paper surveys basic definitions and properties but concentrates on the development of several concrete examples.
LA - eng
KW - filtered rings; associated graded rings; commutative Noetherian domains; schemes; quantum sections; non-commutative quadratic Auslander-regular algebras; gauge algebras; survey; associated Rees rings
UR - http://eudml.org/doc/41746
ER -

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