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 Poincaré-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.
| Autorius: | J. L. Bueso, A. Verschoren, José Gómez-Torrecillas, |
| Serija: | Mathematical Modelling: Theory and Applications |
| Leidėjas: | Springer Netherlands |
| Išleidimo metai: | 2010 |
| Knygos puslapių skaičius: | 316 |
| ISBN-10: | 9048163285 |
| ISBN-13: | 9789048163281 |
| Formatas: | Knyga minkštu viršeliu |
| Kalba: | Anglų |
| Žanras: | Numerical analysis |
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