An abstract characterization of noncommutative projective lines. (English) Zbl 1436.14002
Summary: Let \(k\) be a field. We describe necessary and sufficient conditions for a \(k\)-linear abelian category to be a noncommutative projective line, i.e. a noncommutative \(\mathbb{P}^1\)-bundle over a pair of division rings over \(k\). As an application, we prove that \(\mathbb{P}^1_n\), Piontkovski’s \(n\)th noncommutative projective line [D. Piontkovski, J. Algebra 319, No. 8, 3280–3290 (2008; Zbl 1193.16015)], is the noncommutative projectivization of an \(n\)-dimensional vector space.
MSC:
| 14A22 | Noncommutative algebraic geometry |
| 16S38 | Rings arising from noncommutative algebraic geometry |
Citations:
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