Algorithmic Methods in Non-Commutative Algebra
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.
| Autor: | Bueso, J.L. Gómez-Torrecillas, José Verschoren, A. |
|---|---|
| ISBN: | 9789048163281 |
| Sprache: | Englisch |
| Produktart: | Kartoniert / Broschiert |
| Verlag: | Springer Nature EN |
| Veröffentlicht: | 08.12.2010 |
| Untertitel: | Applications to Quantum Groups |
| Schlagworte: | Algebra Algebraic Geometry Algorithms Associative Rings and Algebras Associative rings C Category Theory, Homological Algebra Category theory (Mathematics) Homological algebra Mathematical foundations Mathematics and Statistics Numeric Computing Numerical analysis Rings (Algebra) |