Sloan P Smith

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A non-commutative space X is a Grothendieck category ModX. We say X is integral if there is an indecomposable injective X-module E X such that its endomorphism ring is a division ring and every X-module is a subquotient of a direct sum of copies of E X. A noetherian scheme is integral in this sense if and only if it is integral in the usual sense. We show(More)
0 Introduction This is a reasonably faithful account of the ve lectures I delivered at the summer course \Geometria Algebraica no Commutativa y Espacios Cuanti-cos" for graduate students, in Spain, July 25{29, 1994. The material covered was, for the most part, an abridged version of Artin and Zhang's paper 2]. Fix a eld k. Given a Z-graded k-algebra, A say,(More)
We give an equivalence of triangulated categories between the derived category of finitely generated representations of symplectic reflection algebras associated with wreath products (with parameter t = 0) and the derived category of coherent sheaves on a crepant resolution of the spectrum of the centre of these algebras.
egalement que l'alg ebre de Sklyanin peut ^ etre d eenie a l'aide des bilin eaires s'annulant sur une certaine sous-vari et e de P 3 P 3 : ABSTRACT. This paper studies point modules and line modules over the algebra deened by E.K. Sklyanin in 17]. It was proved in 21] that the point modules are in bijection with the points of an elliptic curve E in P 3(More)
  • Lieven Le Bruyn, S P Smith, Michel Van Den Bergh
  • 1994
For a 3-dimensional Artin-Schelter-regular algebra A with Hilbert series (1 ? t) ?3 we study central extensions; that is, graded algebras D with a regular central element z in degree 1, such that D=(z) = A. We classify such D and we also classify certain D-modules (point modules and line modules) which proved to be important in the study of 3-dimensional(More)
An amplitude-modulated semiconductor laser is used to excite a 9.2-GHz Raman transition in a cesium atomic beam. Separated-field Ramsey fringes as narrow as 1 kHz wide are observed with a high signal-to-noise ratio, even for semiconductor laser linewidths as wide as 20 MHz. These narrow resonances have potential application in the development of(More)
We study basic properties of Auslander-Gorenstein rings related to duality, localization and purity of minimal injective resolutions. Contents 0. Introduction and deenitions 1. Duality between left and right modules 2. Injective resolutions 3. The Last term of injective resolution. 4. Purity of injective resolutions 5. Examples 6. Localizations 7. Dualities(More)
In 1982 E.K. Sklyanin 13] deened a family of graded algebras A(E;), depending on an elliptic curve E and a point 2 E which is not 4-torsion. Basic properties of these algebras were established in 16], and a study of their representation theory was begun in 7]. The present paper classiies the nite dimensional simple A-modules when is a point of innnite(More)
This paper concerns curves on non-commutative schemes, hereafter called quasi-schemes. A quasi-scheme X is identiied with the category ModX of quasi-coherent sheaves on it. Let X be a quasi-scheme having a regularly embedded hypersurface Y. Let C be a curve on X which is in \good posi-tion" with respect to Y (see Deenition 5.1)|this deenition includes a(More)