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arXiv · 1510.03397

Projective modules and Gr\"obner bases for skew PBW extensions

Oswaldo Lezama·Claudia Gallego
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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 $PBW$ extensions in functional linear systems and in non-commutative algebraic geometry.

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Oswaldo Lezama, Claudia Gallego. 2015-10-12. Projective modules and Gr\"obner bases for skew PBW extensions. https://arxiv.org/abs/1510.03397

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