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Original Articles

Four dimensional regular algebras with point scheme, anonsingular quadric in P3

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Pages 2211-2242 | Received 01 Dec 1995, Published online: 27 Jun 2007

References

  • Alev , J. and Dumas , F. 1994 . Sur le corps des fractions de certaines algèbres quantiques . J. Alg , 170 ( 1 ) : 229 – 265 .
  • Artin , M. 1992 . “ Geometry of quantum planes, azumaya algebras, actions and modules ” . In Contemp. Math Edited by: Haile , D. and Osterburg , J. Vol. 124 , 1 – 15 .
  • Artin , M. and Schelter , W. 1987 . Graded algebras of global dimension 3 . Adv. Math , 66 : 171 – 216 .
  • Artin , M. , Tate , J. and Van Den Bergh , M. 1990 . “ Some algebras associated to automorphisms of elliptic curves ” . In The grothendieck festschrift , Vol. 1 , Birkhäuser .
  • Artin , M. , Tate , J. and Van Den Bergh , M. 1991 . Modules over regular algebras of dimension 3 . Invent math , 106 : 335 – 388 .
  • Cohn , P.M. 1977 . Algebra , Vol. 2 , John wiley & sons .
  • Hartshorne , R. 1977 . “ Algebraic geometry ” . In Grad. Texts in math , Vol. 52 , New York : springer-verlag . Heidelberg
  • Lam , T.Y. 1973 . “ The algebraic theory of quadratic forms ” . In Math. Lee. Note series, W.A , Reading, mass : Benjamin .
  • Le Bruyn , L. 1995 . Central singularities of quantum spaces . J. Alg , 177 : 142 – 153 .
  • Le Bruyn , L. and Smith , S.P. 1993 . Homogenized sl(2) . Proc. Amer. Math. Soc , 118 : 725 – 730 .
  • Le Bruyn , L. , Smith , S.P. and Van Den Bergh , M. 1996 . Central extensions of three dimensional artin-schelter regular algebras . Mathematische zeitschrift , 222 : 171 – 212 .
  • Le Bruyn , L. and Van Den Bergh , M. 1993 . On quantum spaces of lie algebras . Proc. Amer. Math. Soc , 119 ( 2 ) : 407 – 414 .
  • Levasseur , T. and Smith , S.P. 1993 . Modules over the 4-dimensional sklyanin algebra . Bull. Soc. Math. de France , 121 ( 2 ) : 35 – 90 .
  • Nastasescu , C. and Van Oystaeyen , F. 1982 . library of math , Vol. 28 , Amsterdam : North-Holland .
  • Shelton , B. and Vancliff , M. 1999 . Embedding a quantum rank three quadric in a quantum P3 . Comm. Alg , 27 ( 6 ) : 2877 – 2904 .
  • Shelton , B. and Vancliff , M. 1999 . Schemes of line modules in preparation
  • Smith , S.P. and Stafford , J.T. 1992 . Regularity of the four dimensional sklyanin algebra . Compositio math , 83 ( 3 ) : 259 – 289 .
  • Smith , S.P. and Tate , J. 1994 . The center of the 3-dimensional and 4-dimensional sklyanin algebras . J. K-theory , 8 ( 3 ) : 19 – 63 .
  • Stafford , J.T. 1994 . Auslander-regular algebras and maximal orders . J. London math. Soc , 50 ( 2 ) : 276 – 292 . Second Series
  • Vancliff , M. 1994 . Quadratic algebras associated with the union of a quadric and a line in P3 . J. Alg , 165 ( 1 ) : 63 – 90 .
  • Vancliff , M. 1995 . The defining relations of quantum n × n matrices . J. London math. Soc , 52 ( 2 ) : 255 – 262 .
  • Vancliff , M. and Van Rompay , K. 1997 . Embedding a quantum nonsingular quadric in a quantum i P3 . J. Alg , 195 ( 1 ) : 93 – 129 .
  • Van Rompay , K. 1996 . Segre product of artin-schelter regular algebras of dimension 2 and embeddings in quantum P3’s . J. Alg , 180 ( 2 ) : 483 – 512 .
  • Van Rompay , K. march 1996 . “ Embedding quantum quadrics in quantum P3 ” . In Ph.D. Dissertation , march , University of Antwerp UIA .

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