07 Nov 2001

The slogan of the day is "Quantize everything!". The time has come to quantize K-theory. K-functors of a commutative algebra have a structure of a graded ring. Such a structure for non-commutative case has not been constructed before our joint paper with V. Lychagin. It turns out that for some algebras very far from being commutative, their K-theory admits a product structure. The involved algebras are constructed by means of quantum groups. We give an overview of the main ideas, and formulate possible generalizations and applications, with special accent on the problems that can be done by "hovedfagsstudenter" in their "hovedfagsoppgave".