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Examples in non-commutative projective geometry

Published online by Cambridge University Press:  24 October 2008

J. T. Stafford  and
J. J. Zhang
J. T. Stafford
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, U.S.A.
J. J. Zhang
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, U.S.A.
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Extract

Let A = k ⊕ ⊕n ≥ 1An connected graded, Noetherian algebra over a fixed, central field k (formal definitions will be given in Section 1 but, for the most part, are standard). If A were commutative, then the natural way to study A and its representations would be to pass to the associated projective variety and use the power of projective algebraic geometry. It has become clear over the last few years that the same basic idea is powerful for non-commutative algebras; see, for example, [ATV1, 2], [AV], [Sm], [SS] or [TV] for some of the more significant applications. This suggests that it would be profitable to develop a general theory of ‘non-commutative projective geometry’ and the foundations for such a theory have been laid down in the companion paper [AZ]. The results proved there raise a number of questions and the aim of this paper is to provide negative answers to several of these.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 3 , November 1994 , pp. 415 - 433
Copyright
Copyright © Cambridge Philosophical Society 1994

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