Noncommutative Gröbner Bases and Filtered-Graded Transfer
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Beschreibung
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 supplementary material: sn.pub/extras
Autor*in
Huishi Li
Themen in »Noncommutative Gröbner Bases and Filtered-Graded Transfer«
Filtered ring Gradedring Groebner basis Monomial ordering Solvable polynomial algebra algorithms
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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."
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