"Resolutions of Newtonian coalgebras"

Michael Slone
University of Kentucky

Monday, April 10, 2006
4:00 pm, 845 Patterson Office Tower

Abstract:

Newtonian coalgebras are special structures which arise naturally in the study of the cd-index of polytopes and the ab-index of graded posets. In 2002, Ehrenborg and Readdy defined a homology for nicely graded Newtonian coalgebras and used it to reprove the existence of the cd-index. The homology is a special case of Hochschild cohomology for coalgebras. We will explain the connection between Newtonian homology and Hochschild cohomology. We will also discuss Kobayashi's algorithm for computing a resolution of an ideal in a free associative algebra admitting a Gr\"obner base and indicate how this can be dualized to give a method for computing Newtonian homology of finitely generated ideals of Newtonian coalgebras.