Noncommutative Gröbner Bases and Filtered-Graded Transfer

Huishi Li (auth.)3540441964, 9783540441960

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