Projective modules and Gr\"obner bases for skew PBW extensions
Rings and Algebras
2015-10-13 v1
Abstract
Many rings and algebras arising in quantum mechanics, algebraic analysis, and non-commutative algebraic geometry can be interpreted as skew PBW (Poincar\'e-Birkhoff-Witt) extensions. In the present paper we study two aspects of these non-commutative rings: its finitely generated projective modules from a matrix-constructive approach, and the construction of the Gr\"obner theory for its left ideals and modules. These two topics could be interesting in future eventual applications of skew extensions in functional linear systems and in non-commutative algebraic geometry.
Cite
@article{arxiv.1510.03397,
title = {Projective modules and Gr\"obner bases for skew PBW extensions},
author = {Oswaldo Lezama and Claudia Gallego},
journal= {arXiv preprint arXiv:1510.03397},
year = {2015}
}