Highly Influential

3 Excerpts

- Published 2010

The incidence category CF of a family F of colored posets closed under disjoint unions and the operation of taking convex sub-posets was introduced by the author in [12], where the Ringel-Hall algebra HF of CF was also defined. We show that if the Hasse diagrams underlying F are rooted trees, then the subspace nF of primitive elements of HF carries a pre-Lie structure, defined over Z, and with positive structure constants. We give several examples of nF , including the nilpotent subalgebras of sln, Lgln, and several others.

@inproceedings{Szczesny2010PrelieAA,
title={Pre-lie Algebras and Incidence Categories of Colored Rooted Trees},
author={Matt Szczesny and Murray Gerstenhaber},
year={2010}
}