Non-commutative Groebner technology, its implementation and applications | Department of Mathematics

Non-commutative Groebner technology, its implementation and applications

Event Information
Event Location: 
GAB 406, 4-5 PM; Refreshments: GAB 472, 3:30 PM
Event Date: 
Monday, November 8, 2010 - 4:00pm

In this talk we give an overview of an important part of computer algebra, relying on the concept of Groebner basis. This concept exists in very general settings, including the one of free associative algebras over a fixed field. We will define a nice category of so-called $G$-algebras, demonstrate their properties and introduce Groebner bases for them. The notion of Gel'fand-Kirillov dimension will be introduced, as well as the algorithm for its computation. A special attention will be paid to the nice homological properties of such algebras. A particular application is the computation of the preimage of a left ideal under a morphism of two $G$-algebras, which relies heavily on Groebner technology. We will show the implementation of Groebner technology for different classes of non-commutative algebras in a computer algebra system SINGULAR (www.singular.uni-kl.de, note that it is freely available) and perform some computations live. If the time allows, we can discuss several ongoing projects concerning algebraic analysis and $D$-modules, homological algebra, and polynomial modeling of signals.