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arXiv · 1908.04880

Some open problems in the context of skew PBW extensions and semi-graded rings

Oswaldo Lezama
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Abstract

In this paper we discuss some open problems of non-commutative algebra and non-commutative algebraic geometry from the approach of skew $PBW$ extensions and semi-graded rings. More exactly, we will analyze the isomorphism arising in the investigation of the Gelfand-Kirillov conjecture about the commutation between the center and the total ring of fractions of an Ore domain. The Serre's conjecture will be discussed for a particular class of skew $PBW$ extensions. The questions about the noetherianity and the Zariski cancellation property of Artin-Schelter regular algebras will be reformulated for semi-graded rings. Advances for the solution of some of the problems are included.

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Oswaldo Lezama. 2019-08-13. Some open problems in the context of skew PBW extensions and semi-graded rings. https://arxiv.org/abs/1908.04880

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