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Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups

Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups
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Field name Details
Dewey Class 518
Title Algorithmic Methods in Non-Commutative Algebra ([EBook] :) : Applications to Quantum Groups / / by José Bueso, José Gómez-Torrecillas, Alain Verschoren.
Author Bueso, José
Added Personal Name Gómez-Torrecillas, José author.
Verschoren, Alain author.
Other name(s) SpringerLink (Online service)
Publication Dordrecht : : Springer Netherlands : : Imprint: Springer, , 2003.
Physical Details XI, 300 p. : online resource.
Series Mathematical modelling : theory and applications 1386-2960 ; ; 17
ISBN 9789401702850
Summary Note 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.:
Contents note 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-94-017-0285-0
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