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AuthorLi, Huishi. author
TitleNoncommutative Grรถbner Bases and Filtered-Graded Transfer [electronic resource] / by Huishi Li
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2002
Connect tohttp://dx.doi.org/10.1007/b84211
Descript IX, 202 p. online resource

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


CONTENT

Introduction -- Chapter I: Basic Structural Tricks and Examples -- Chapter II: Grรถbner Bases in Associative Algebras -- Chapter III: Grรถbner Bases and Basic Algebraic-Algorithmic Structures -- Chapter IV: Filtered-Graded Transfer of Grรถbner 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


Mathematics Associative rings Rings (Algebra) Algorithms Mathematics Associative Rings and Algebras Algorithms



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