| Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups 2003 Edition Contributor(s): Bueso, J. L. (Author), Gómez-Torrecillas, José (Author), Verschoren, A. (Author) |
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ISBN: 1402014023 ISBN-13: 9781402014024 Publisher: Springer OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: July 2003 |
| Additional Information |
| BISAC Categories: - Computers | Computer Science - Mathematics | Geometry - Algebraic - Computers | Programming - Algorithms |
| Dewey: 512.55 |
| LCCN: 2003052014 |
| Series: Mathematical Modelling: Theory and Applications |
| Physical Information: 0.8" H x 6.4" W x 9.4" (1.35 lbs) 300 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups. One of the fundamental properties of quantum groups is that they are modelled by associative coordinate rings possessing a canonical basis, which allows for the use of algorithmic structures based on Groebner bases to study them. This book develops these methods in a self-contained way, concentrating on an in-depth study of the notion of a vast class of non-commutative rings (encompassing most quantum groups), the so-called Poincar -Birkhoff-Witt rings. We include algorithms which treat essential aspects like ideals and (bi)modules, the calculation of homological dimension and of the Gelfand-Kirillov dimension, the Hilbert-Samuel polynomial, primality tests for prime ideals, etc. |