EPSRC Grant GR/M52656/01, Summary of Final Report Representation Theory of Noncommutative Algebras PI T H Lenagan,

This Overseas Travel Grant was awarded to enable the Principal Investigator to participate in the Program on Noncommutative Algebra (Fall 1999 - Spring 2000) at the Mathematical Sciences Research Institue (MSRI), in Berkeley, California. The programme focused on recent developments in noncommutative algebraic geometry, Hopf algebras, quantum groups, Lie and Jordan algebras and classical ring theory. The organisers of the programme were M Artin, S Montgomery, C Procesi, L Small, J T Stafford and E Zelmanov.

The Principal Investigator spent a period of two months (February and March, 2000) at MSRI. In addition to conducting is own research and meeting some of his main collaborators, he was able to attend many lectures by leading experts in the fields covered by the programme and to have extended discussions on many topics of current interest in noncommutative algebra and noncommutative algebraic geometry.

Results were obtained in joint work with Goodearl on H-primes in quantum matrices, with Rigal on quantum determinantal ideals and factors, and with Bavula on Krull dimension of Generalized Weyl Algebras. These are all parts of continuing research collaborations. Some of the results obtained are available in preprints on the Principal Investigators webpage at

http://www.maths.ed.ac.uk/~tom

and others will be posted there on the completion of the research.