Algebraic Combinatorics Seminar
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UNIVERSITY OF KENTUCKY **

ALGEBRAIC COMBINATORICS SEMINAR

845 PATTERSON OFFICE TOWER

SPRING 2006

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"Resolutions of Newtonian coalgebras"

Michael Slone

University of Kentucky

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Monday, April 10, 2006

4:00 pm, 845 Patterson Office Tower

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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.