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Noncommutative Gröbner Bases and Filtered-Graded Transfer / by Huishi Li
(Lecture Notes in Mathematics. ISSN:16179692 ; 1795)
版 | 1st ed. 2002. |
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出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
出版年 | 2002 |
大きさ | IX, 202 p : online resource |
著者標目 | *Li, Huishi author SpringerLink (Online service) |
件 名 | LCSH:Associative rings LCSH:Associative algebras LCSH:Algorithms FREE:Associative Rings and Algebras FREE:Algorithms |
一般注記 | 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 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 HTTP:URL=https://doi.org/10.1007/b84211 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783540457657 |
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EB00210817 |
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