Synopses & Reviews
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.
Includes bibliographical references (p. -193) and index.
Table of Contents
Introduction.- Chapter I: Basic Structural Tricks and Examples.- Chapter II: Gröbner Bases in Associative Algebras.- Chapter III: Gröbner Bases and Basic Algebraic-Algorithmic Structures.- Chapter IV: Filtered-Graded Transfer of Gröbner Bases.- Chapter V: GK-dimension of Modules over Quadric Solvable Polynomial Algebras and Elimination of Variables.- Chapter VI: Multiplicity Computation of Modules over Quadric Solvable Polynomial Algebras.- Chapter VII: (partial-)Holonomic Modules and Functions over Quadric Solvable Polynomial Algebras.- Chapter VII: Regularity and Ko-group of Quadric Solvable Polynomial Algebras.- References.- Index.