Noncommutative Gröbner Bases and Filtered-Graded Transfer

✍ Scribed by Huishi Li (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2002
• Tongue: English
• Leaves: 192
• Series: Lecture Notes in Mathematics 1795
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Introduction....Pages 1-4
CHAPTER I: Basic Structural Tricks and Examples....Pages 5-32
CHAPTER II: Gröbner Bases in Associative Algebras....Pages 33-65
CHAPTER III: Gröbner Bases and Basic Algebraic-Algorithmic Structures....Pages 67-90
CHAPTER IV: Filtered-Graded Transfer of Gröbner Bases....Pages 91-105
CHAPTER V: GK-dimension of Modules over Quadric Solvable Polynomial Algebras and Elimination of Variables....Pages 107-132
CHAPTER VI: Multiplicity Computation of Modules over Quadric Solvable Polynomial Algebras....Pages 133-151
CHAPTER VII: ( $\partial$ )-Holonomic Modules and Functions over Quadric Solvable Polynomial Algebras....Pages 153-173
CHAPTER VIII: Regularity and K 0 -group of Quadric Solvable Polynomial Algebras....Pages 175-186
References....Pages 187-193
Index....Pages 195-197

✦ Subjects

Associative Rings and Algebras; Algorithms