CROSSED MODULES OF ALGEBRAS WITH GAP (Group, Algorithm and Programming)

Alper Odabaş

Computer Science,

PhD Thesis, 2009

Thesis Adviser: Prof. Dr. Zekeriya Arvasi

SUMMARY

The powerful computer algebra system GAP provides a high level programming language with several advantages for coding of new mathematical structures. The GAP system has been developed over the last 20 year at RWTH in Aachen, Germany. It has a highly developed, easy to understand programming language, incorporated. It is especially powerful for group theory. Crossed modules introduced by Whitehead is one of important algebraic system. The GAP share package on crossed modules over group, XMOD, has been developed at Bangor, Wales, UK by Wensley and Alp. Crossed module may be thought of as 2-dimensional groups for solving several physical problems and for giving new ideas related to many mathematical structures. A number of phenomena in group theory are better seen from a crossed module point of view, Crossed modules also occurs commutative algebra and Quantum field theory in physics. The main objective of this thesis is to add a new share package which includes many functions to the GAP and to develop in the direction of application to higher scalar crossed modules and to give some analogue to other algebraic systems such as commutative algebras. This facilities will be important for specific calculations in combinatorial algebra theory and in simplicial theory which is an important tool in algebraic topology. This also given many applications to theoretical computer algebra. The thesis to be carried out along these objectives mentioned above is to build the future of computational mathematics and to link with actual research projects in a range of pure and applied topics in which algebra is a key part.