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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.
List 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 SolvablePolynomial 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.
Summary
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.
Additional text
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."
Report
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."
