Ebook: Noncommutative Gröbner Bases and Filtered-Graded Transfer

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.

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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.

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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.
Content:
Introduction....Pages 1-4
CHAPTER I: Basic Structural Tricks and Examples....Pages 5-32
CHAPTER II: Gr?bner Bases in Associative Algebras....Pages 33-65
CHAPTER III: Gr?bner Bases and Basic Algebraic-Algorithmic Structures....Pages 67-90
CHAPTER IV: Filtered-Graded Transfer of Gr?bner 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

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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.
Content:
Introduction....Pages 1-4
CHAPTER I: Basic Structural Tricks and Examples....Pages 5-32
CHAPTER II: Gr?bner Bases in Associative Algebras....Pages 33-65
CHAPTER III: Gr?bner Bases and Basic Algebraic-Algorithmic Structures....Pages 67-90
CHAPTER IV: Filtered-Graded Transfer of Gr?bner 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
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