An abstract characterization of noncommutative projective lines

  • Adam Nyman

    Western Washington University, Bellingham, USA
An abstract characterization of noncommutative projective lines cover
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Abstract

Let kk be a field.We describe necessary and sufficient conditions for a kk-linear abelian category to be a noncommutative projective line, i.e. a noncommutative P1\mathbb P^1-bundle over a pair of division rings over kk. As an application, we prove that Pn1\mathbb P^1_n, Piontkovski’s nnth noncommutative projective line, is the noncommutative projectivization of an nn-dimensional vector space.

Cite this article

Adam Nyman, An abstract characterization of noncommutative projective lines. J. Noncommut. Geom. 13 (2019), no. 2, pp. 517–552

DOI 10.4171/JNCG/329