A Serre-type category equivalence is claimed for semi-graded rings under a noetherian and underexplained X1 condition, and a degenerate class of semi-graded Artin-Schelter algebras is identified.
An introduction to Noncommutative Projective Geometry
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abstract
These notes are an expanded version of the author's lectures at the graduate workshop "Noncommutative Algebraic Geometry" at the Mathematical Sciences Research Institute in June 2012. The main topics discussed are Artin-Schelter regular algebras, point modules, and the noncommutative projective scheme associated to a graded algebra.
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Some open problems in the context of skew PBW extensions and semi-graded rings
A Serre-type category equivalence is claimed for semi-graded rings under a noetherian and underexplained X1 condition, and a degenerate class of semi-graded Artin-Schelter algebras is identified.