Equivalences for noncommutative projective spaces

Abstract

Following Artin and Zhang's formulation of noncommutative projective geometry, we classify up a family of skew polynomial quadratic algebras up to graded Morita equivalence and their corresponding noncommutative projective spaces up to birational equivalences. We also study their point varieties and provide examples of non-isomorphic noncommutative projective spaces.

arXiv commentNew version containing important corrections. The last theorem of the previous version was removed due to a gap in its proof

Cited by in corpus (4)

• The isomorphism problem for quantum affine spaces, homogenized quantized Weyl algebras, and quantum matrix algebras
• The point variety of quantum polynomial rings
• On Knörrer periodicity for quadric hypersurfaces in skew projective spaces
• Combinatorial classification of $(\pm 1)$-skew projective spaces