Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/3978
Title: Ideals of cubic algebras and an invariant ring of the Weyl algebra
Authors: DE NAEGHEL, Koen 
Marconnet, N
Issue Date: 2007
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Source: JOURNAL OF ALGEBRA, 311(1). p. 380-433
Abstract: We classify reflexive graded right ideals, up to isomorphism and shift, of generic cubic three-dimensional Artin-Schelter regular algebras. We also determine the possible Hilbert functions of these ideals. These results are obtained by using similar methods as for quadratic Artin-Schelter algebras [K. DE NAEGHEL, M. VAN DEN BERGH, Ideal classes of three-dimensional Sklyanin algebras, J. Algebra 276 (2) (2004) 515-551; K. DE NAEGHEL, M. VAN DEN BERGH, Ideal classes of three dimensional Artin-Schelter regular algebras, J. Algebra 283 (1) (2005) 399-429]. In particular our results apply to the enveloping algebra of the Heisenberg-Lie algebra from which we deduce a classification of right ideals of the invariant ring A(1)(<rho >) of the first Weyl algebra A(1) = k < x, y >/(xy - yx - 1) under the automorphism rho(x) = -x, rho(y) = -y.
Notes: Hasselt Univ, Dept WNI, B-3590 Diepenbeek, Belgium. Univ Antwerp, Dept Wiskunde Informat, B-2020 Antwerp, Belgium.DE NAEGHEL, K, Hasselt Univ, Dept WNI, Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium.koendenaeghel@hotmail.com nicolas.marconnet@ua.ac.be
Keywords: Weyl algebra; enveloping algebra of the Heisenberg-Lie algebra; quantum quadric; ideals; Hilbert series
Document URI: http://hdl.handle.net/1942/3978
ISSN: 0021-8693
e-ISSN: 1090-266X
DOI: 10.1016/j.jalgebra.2006.11.015
ISI #: 000246049400021
Category: A1
Type: Journal Contribution
Validations: ecoom 2008
Appears in Collections:Research publications

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