Algorithmic Methods in Non-Commutative Algebra

Applications to Quantum Groups

J.L. Bueso, José Gómez-Torrecillas, A. Verschoren (Autoren)

Buch | Hardcover

300 Seiten

2003
Springer-Verlag New York Inc.
978-1-4020-1402-4 (ISBN)

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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.

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.

Erscheint lt. Verlag	31.7.2003
Reihe/Serie	Mathematical Modelling: Theory and Applications ; 17
Zusatzinfo	XI, 300 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	156 x 234 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	1-4020-1402-3 / 1402014023
ISBN-13	978-1-4020-1402-4 / 9781402014024
Zustand	Neuware