The geometry of arithmetic noncommutative projective lines

2013/08/23 by Nyman, Adam · 1 citation
#FOS: Mathematics #Primary 14A22 #Quantum Algebra (math.QA) #Secondary 16S38

paper · doi:10.48550/arxiv.1308.5185

Abstract

Let k be a perfect field and let K/k be a finite extension of fields. An arithmetic noncommutative projective line is a noncommutative space equal to the projectivization of the noncommutative symmetric algebra of a k-central two -sided vector space of rank two over K. We study the geometry of these spaces. More precisely, we prove they are integral, we classify vector bundles over them, we classify them up to isomorphism, and we classify isomorphisms between them. Using the classification of isomorphisms, we compute the automorphism group of an arithmetic noncommutative projective line.

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• Coherent I-indexed algebras and noncommutative projective schemes

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