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.
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris 1795 3 Berlin Heidelberg New York Hong Kong London Milan Paris Tokyo Huishi Li Noncommutative Gröbner Bases and Filtered-Graded Transfer 13 Author Huishi LI Department of Mathematics Bilkent University P.O. Box 217 06533 Ankara Turkey e-mail:
[email protected] http://www.fen.bilkent.edu.tr/˜huishi Cataloging-in-Publication Data applied for Bibliograhpic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de Mathematics Subject Classification (2000): 16Z05, 68W30, 16W70, 16S99 ISSN 0075-8434 ISBN 3-540-44196-4 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the materi