![Algorithmic Methods in Non-Commutative Algebra [electronic resource] : Applications to Quantum Groups /](/search/themes/bootstrap3/images/libros.png)
Algorithmic Methods in Non-Commutative Algebra [electronic resource] : Applications to Quantum Groups /
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.
| Main Authors: | , , , |
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| Format: | Texto biblioteca |
| Language: | eng |
| Published: |
Dordrecht : Springer Netherlands : Imprint: Springer,
2003
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| Subjects: | Computer science., Numerical analysis., Algebraic geometry., Associative rings., Rings (Algebra)., Category theory (Mathematics)., Homological algebra., Algorithms., Computer Science., Numeric Computing., Associative Rings and Algebras., Category Theory, Homological Algebra., Algebraic Geometry., |
| Online Access: | http://dx.doi.org/10.1007/978-94-017-0285-0 |
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| Summary: | 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. |
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