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Two applications of noncommutative Groebner bases

Two applications of noncommutative Groebner bases In this paper, by using the noncommutative Groebner bases in the sense of Mora, we first give an algorithmic description of the defining relations of a quadric algebra with a PBW basis, which enables us to use Berger’sq-Jacobi condition in a more general extent; and secondly, we give an algorithmic determination of the defining relations of the associated graded algebras of a given algebra with given defining relations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL UNIVERSITA DI FERRARA Springer Journals

Two applications of noncommutative Groebner bases

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Publisher
Springer Journals
Copyright
Copyright © Università degli Studi di Ferrara 1999
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/bf02825942
Publisher site
See Article on Publisher Site

Abstract

In this paper, by using the noncommutative Groebner bases in the sense of Mora, we first give an algorithmic description of the defining relations of a quadric algebra with a PBW basis, which enables us to use Berger’sq-Jacobi condition in a more general extent; and secondly, we give an algorithmic determination of the defining relations of the associated graded algebras of a given algebra with given defining relations.

Journal

ANNALI DELL UNIVERSITA DI FERRARA – Springer Journals

Published: Jan 1, 1999

Keywords: Standard Basis; Free Algebra; Homogeneous Element; Weyl Algebra; General Extent

References

  • An extension of Buchberger’s algorithm and calculations in enveloping fields of Lie algebras
    Apel, J.; Lassner, W.
  • The quantum Poincaré-Birkhoff-Witt Theorem
    Berger, R.
  • Non-commutative Groebner bases in algebras of solvable type
    Kandri-Rody, A.; Weispfenning, V.
  • On quantum spaces of Lie algebras
    Le Bruyn, L.; van den Bergh, M.
  • Homogenized sl(2)
    Le Bruyn, L.; Smith, S. P.
  • Dehomogenization of gradings to Zariskian filtrations and applications to invertible ideals
    Huishi, Li; van Oystaeyen, F.
  • An introduction to commutative and noncommutative Groebner bases
    Mora, T.