Algorithmic Methods in Non-Commutative Algebra
Subtitle: Applications to Quantum Groups
By: by José Bueso, José Gómez-Torrecillas, Alain Verschoren
Contributors: Gómez-Torrecillas, José; Verschoren, Alain
Series: Mathematical Modelling, Theory and Applications -- 17; Mathematical Modelling, Theory and Applications -- 17
Publisher: Springer Netherlands
Published: 2003
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 300
ISBN-13: 9789048163281; 9789401702850
Subjects: Electronic data processing; Geometry, algebraic; Algorithms; Computer science; Algebra
Description: 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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