arXiv subjects
Publications and source records attributed to Silu Liu.
In this note, we prove that, under Kabbaj's weighted polynomial Hilbert-series hypothesis, every $N$-Koszul graded algebra of finite global dimension with $N>2$ is necessarily $3$-Koszul of global dimension $3$.
We prove that all noetherian PI Artin--Schelter regular algebras of dimension $3$ are unique factorization rings. In a certain sense, this result is a noncommutative analogue to the fact that regular local rings of dimension 3 are UFDs. The fact constitutes a crucial component in the proof of the assertion that all regular local rings are UFDs, known as the Auslander--Buchsbaum theorem.
We prove that the ozone group of any PI Artin-Schelter regular algebra is abelian, which answers a question of Chan-Gaddis-Won-Zhang. For any Calabi-Yau PI Artin-Schelter regular algebra, we prove that the homological determinant of its ozone group acting on it is trivial.