Projective modules and Gröbner bases for skew PBW extensions
Volume 521 / 2017
Dissertationes Mathematicae 521 (2017), 1-50
MSC: Primary 16Z05; Secondary 16D40, 15A21.
DOI: 10.4064/dm747-4-2016
Published online: 23 January 2017
Abstract
Many rings and algebras arising in quantum mechanics, algebraic analysis, and non-commutative algebraic geometry can be interpreted as skew PBW (Poincaré–Birkhoff–Witt) extensions. In the present paper we study two aspects of these non-commutative rings: their finitely generated projective modules from a matrix-constructive approach, and the construction of the Gröbner theory for their left ideals and modules. These two topics have interesting applications in functional linear systems and in non-commutative geometry.
