Algorithmic Methods in Non-Commutative Algebra

Applications to Quantum Groups
1. Auflage. Softcover version of original hardcover Auflage 2003
ISBN: 978-90-481-6328-1
Verlag: Springer Netherlands

Buch, Englisch, 300 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 482 g

Reihe: Mathematical Modelling: Theory and Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Bueso, J. L.

Verschoren, A.

Gómez-Torrecillas, José

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik EDV | Informatik Informatik
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

1. Generalities on rings.- 2. Gröbner basis computation algorithms.- 3. Poincaré-Birkhoff-Witt Algebras.- 4. First applications.- 5. Gröbner bases for modules.- 6. Syzygies and applications.- 7. The Gelfand-Kirillov dimension and the Hilbert polynomial.- 8. Primality.- References.