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Noncommutative Gröbner Bases and Filtered-Graded Transfer

  • Book
  • © 2002

Overview

Authors:
  1. Huishi Li
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1795)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Huishi Li
    Pages 1-4

  3. CHAPTER I: Basic Structural Tricks and Examples

    • Huishi Li
    Pages 5-32

  4. CHAPTER II: Gröbner Bases in Associative Algebras

    • Huishi Li
    Pages 33-65

  5. CHAPTER III: Gröbner Bases and Basic Algebraic-Algorithmic Structures

    • Huishi Li
    Pages 67-90

  6. CHAPTER IV: Filtered-Graded Transfer of Gröbner Bases

    • Huishi Li
    Pages 91-105

  7. CHAPTER V: GK-dimension of Modules over Quadric Solvable Polynomial Algebras and Elimination of Variables

    • Huishi Li
    Pages 107-132

  8. CHAPTER VI: Multiplicity Computation of Modules over Quadric Solvable Polynomial Algebras

    • Huishi Li
    Pages 133-151

  9. CHAPTER VII: ()-Holonomic Modules and Functions over Quadric Solvable Polynomial Algebras

    • Huishi Li
    Pages 153-173

  10. CHAPTER VIII: Regularity and K0-group of Quadric Solvable Polynomial Algebras

    • Huishi Li
    Pages 175-186

  11. References

    • Huishi Li
    Pages 187-193

  12. Index

    • Huishi Li
    Pages 195-197

  13. Back Matter

    Pages 199-202
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Keywords

About this book

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.

Reviews

From the reviews:

MATHEMATICAL REVIEWS

"The monograph covers an important area of research, and the material included may be helpful for researchers and graduate students interested in developing and using Grobner bases in solutions to various mathematical problems. References to many existing computer algebra systems enable the readers to verify methods introduced in this book with the help of computers."

Bibliographic Information

  • Book Title: Noncommutative Gröbner Bases and Filtered-Graded Transfer

  • Authors: Huishi Li

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b84211

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Softcover ISBN: 978-3-540-44196-0Published: 23 October 2002

  • eBook ISBN: 978-3-540-45765-7Published: 19 October 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: IX, 202

  • Topics: Associative Rings and Algebras, Algorithms

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