Noncommutative Gröbner Bases and Filtered-Graded Transfer

  • Authors
  • Huishi Li

Part of the Lecture Notes in Mathematics book series (LNM, volume 1795)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Huishi Li
    Pages 1-4
  3. CHAPTER VII: (Open image in new window)-Holonomic Modules and Functions over Quadric Solvable Polynomial Algebras
    Huishi Li
    Pages 153-173
  4. Huishi Li
    Pages 187-193
  5. Huishi Li
    Pages 195-197
  6. Back Matter
    Pages 199-202

About this book

Introduction

This self-contained monograph is the first to feature the intersection of the structure theory of noncommutative associative algebras and the algorithmic aspect of Groebner basis theory. A double filtered-graded transfer of data in using noncommutative Groebner bases leads to effective exploitation of the solutions to several structural-computational problems, e.g., an algorithmic recognition of quadric solvable polynomial algebras, computation of GK-dimension and multiplicity for modules, and elimination of variables in noncommutative setting. All topics included deal with algebras of (q-)differential operators as well as some other operator algebras, enveloping algebras of Lie algebras, typical quantum algebras, and many of their deformations.

Keywords

Filtered ring Gradedring Groebner basis Monomial ordering Solvable polynomial algebra algorithms

Bibliographic information

  • DOI https://doi.org/10.1007/b84211
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-44196-0
  • Online ISBN 978-3-540-45765-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book